{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "单分量MH算法，简单来说就是对高维随机变量遍历其每一个维度，并对每个维度单独进行采样，这样就将一个复杂的采样问题分拆成了一个个更加简单的采样问题，聪明童鞋可能已经想到了，要怎么操作才能保证细致平衡方程成立勒，这就需要用到**满条件分布**咯，它将会为我们的单个维度采样打开大门，下面先说明一下"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一.满条件分布\n",
    "MCMC的目标分布通常是多元的联合概率分布$p(x)=p(x_1,x_2,...,x_k)$，其中$x=(x_1,x_2,...,x_k)^T$为$k$维随机变量。如果条件概率分布$p(x_I\\mid x_{-I})$中所有$k$个变量全部出现，其中$x_I=\\{x_i,i\\in I\\},x_{-I}=\\{x_i,i\\notin I\\},I\\subset K=\\{1,2,...,k\\}$，那么称这种条件概率分布为满条件分布。   \n",
    "\n",
    "满条件分布有一个非常有用的性质，那就是对于随机变量的任意取值$x,x'$，和任意的$I\\subset K$，以下等式成立：    \n",
    "\n",
    "$$\n",
    "\\frac{p(x'_I\\mid x'_{-I})}{p(x_I\\mid x_{-I})}=\\frac{p(x')}{p(x)}\n",
    "$$   \n",
    "\n",
    "惊不惊喜，意不意外，有了上面的等式那就意味着对$\\frac{p(x')}{p(x)}$的计算，只需落到对单个维度上的条件概率进行计算即可！这在方便联合概率之比的计算的同时也为单分量MH算法提供了理论支撑，下面先简单推导一下上面的等式为什么成立：    \n",
    "\n",
    "$$\n",
    "p(x_I\\mid x_{-I})=\\frac{p(x)}{p(x_{-I})}=\\frac{p(x)}{\\int_{x_I}p(x)dx_I}\\propto p(x)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二.单分量MH算法\n",
    "在写具体算法之前，先对相应的符号表达做个解释：   \n",
    "\n",
    "（1）设在第$i$次迭代结束时分量$x_j$的取值为$x_j^{(i)}$，其中$j=1,2,...,k,i=0,1,2,...$；   \n",
    "\n",
    "（2）$x_{-j}^{(i)}$表示在第$i$轮，更新到第$j-1$维时，除去第$j$维后的所有值，即前$j-1$维已经更新为第$i$轮的值，而$j+1$维直至最后维都还是$i-1$轮的值，即：   \n",
    "\n",
    "$$\n",
    "x_{-j}^{(i)}=(x_1^{i},...x_{j-1}^i,x_{j+1}^{(i-1)},...x_k^{(i-1)})^T\n",
    "$$  \n",
    "\n",
    "好了，可以描述算法流程了\n",
    "\n",
    "#### 单分量MH算法流程\n",
    "输入：目标概率分布的密度函数$p(x)$，正整数$m,n,m<n$；   \n",
    "输出：$p(x)$的随机样本$x_{m+1},x_{m+2},...,x_n$\n",
    "\n",
    ">（1）初始化样本$x^{(0)}=(x_1^{(0)},x_2^{(0)},...,x_k^{(0)})$   \n",
    "\n",
    ">（2）对$i=1,2,...,m,m+1,...n$：   \n",
    "\n",
    ">>对$j=1,2,...,k$：   \n",
    "\n",
    ">>>（2.1）根据建议分布$q(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})$抽样第$j$维的候选值$x_j^{'(i)}$   \n",
    "\n",
    ">>>（2.2）计算第$j$维的接收率：   \n",
    "$$\n",
    "\\alpha(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})=min\\{1,\\frac{p(x_j^{'(i)}\\mid x_{-j}^{(i)})q(x_j^{'(i)}\\rightarrow x_j^{(i-1)}\\mid x_{-j}^{(i)})}{p(x_j^{(i-1)}\\mid x_{-j}^{(i)})q(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})}\\}\n",
    "$$   \n",
    "\n",
    ">>>（2.3）从$(0,1)$均匀分布中随机采样$u$，如果$u<\\alpha(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})$，则令$x_j^{(i)}=x_j^{'(i)}$，否则$x_j^{(i)}=x_j^{(i-1)}$   \n",
    "\n",
    ">（3）返回样本集$\\{x_{m+1},x_{m+2},...,x_n\\}$  \n",
    "\n",
    "完事儿了，要证明单分量MH算法满足细致平衡方程也很简单，下面简单说明一下：    \n",
    "\n",
    "（1）首先条件概率之比$\\frac{p(x_j^{'(i)}\\mid x_{-j}^{(i)})}{p(x_j^{(i-1)}\\mid x_{-j}^{(i)})}$根据满条件分布中的等式可以替换为联合概率之比；   \n",
    "\n",
    "（2）其次，任意建议分布$q(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})$均不会影响到细致平衡方程（见前一个note的证明）；  \n",
    "\n",
    "综合这两条我们可以推导出（下面的$\\sim$表示分布相同）：    \n",
    "\n",
    "$$\n",
    "p(x_1^{(i-1)},x_2^{(i-1)},...,x_k^{(i-1)})\\\\\n",
    "\\sim p(x_1^{(i)},x_2^{(i-1)},...,x_k^{(i-1)})\\\\\n",
    "\\cdots\\\\\n",
    "\\sim p(x_1^{(i)},x_2^{(i)},...x_j^{(i)},x_{j+1}^{(i-1)},...,x_k^{(i-1)})\\\\\n",
    "\\cdots\\\\\n",
    "\\sim p(x_1^{(i)},x_2^{(i)},...,x_k^{(i)})\\\\\n",
    "$$   \n",
    "\n",
    "所以：$p(x_1^{(i-1)},x_2^{(i-1)},...,x_k^{(i-1)})\\sim p(x_1^{(i)},x_2^{(i)},...,x_k^{(i)}),i=1,2,...$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 三.案例\n",
    "由于单分量MH是用于高维空间的采样，所以这里我造一个二元高斯分布$N(u,\\Sigma)$，其对应的均值、协方差如下：   \n",
    "\n",
    "$$\n",
    "u=[0,0]^T\\\\\n",
    "\\Sigma=\\begin{bmatrix}\n",
    "1 &\\rho \\\\ \n",
    "\\rho & 1\n",
    "\\end{bmatrix}\n",
    "$$   \n",
    "\n",
    "那么，它对应的条件概率分布为一元高斯分布，如下：   \n",
    "\n",
    "$$\n",
    "p(x_1\\mid x_2)=N(\\rho x_2,(1-\\rho^2))\\\\\n",
    "p(x_2\\mid x_1)=N(\\rho x_1,(1-\\rho^2))\n",
    "$$  \n",
    "\n",
    "我们不妨取$\\rho=0.5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('../')\n",
    "from ml_models import utils\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#定义均值，协方差\n",
    "u=np.asarray([0,0])\n",
    "sigma=np.asarray([[1,0.5],\n",
    "                  [0.5,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
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bcgl5Xiqy6mRlEhwfzKeHPuWXi7+g1+qZ+8RcXm77coV+FoWx5PgSpuyawm9P/8aIJiMqvb1HEVnYZSqd4rzUczHn+Pzw52y8uhGNUsNzLZ9jWsdpNKxW/MJn4Lko5my7QpIhK21Er1Pz0eCmhc4GUk2pbAvZxqZrm9gZthOj1Yheq+fJ+k8yqMEg+tTtU6ne6cPssRfEpXuXmLprKntv7qVDzQ6sGrqKBlUrtxSAVbTSZnkbUk2phLwect9OkXqUkIVdptIpzEs1Ka7Rutl+gkKDcHVw5dW2r/JWh7fwdPYskd3Ac1FM33gBiy23dbVCYOHTLe3ibrQY2X59O79e/pWg0CBMNhPeLt4Mb5RVbraLX5f7dhDGxjMRvBd4DIM1BREDkmBCrbIyroMP7WpnxepVChVqhRpHtSOuDq7otXqqOVbDWeP8QEITkiSx9tJa3vjjDUw2E98N/I5xLcZVapu7wnbR75d+LBuwjJfavlSpbT2KyMIuU+nk9VIzFVdIUf1KpvI81RyrMbXDVF5r9xpuWrdibe0N30tjj8Z4u3gX6v0CeLs58MkzClZfXM2mq5tIM6fh6ezJyCYjGdl0JB19O1Z4fZjszUjXE65zI/EG4Unh3Eq5xe3U20SnRXM3/W6BB1aXFEe1Iz4uPvjr/alXpR6NqjWiWfVmBHgF2GcZlblQGJUaxZjNYzh46yDvdHyH+b3nV1qNHUmSeOz7x0jOTCb49eD7WsvnUUAWdplKJzvGnmy9QrL6FzKV51BKesY1fZ2lQ2bgpHEq1sax28cYvWk0Dao2QKfW8VKbl3jtBynfTEDEQKpqM+nKvdgUcbhoXHi6ydOMaT6G7rW6FxsjLqkwGi1GLt67yLm757hw9wKX4y5zNe4qicZE+z0CAt4u3vi5+eHt4o2XsxfVnarjrnMn/B4EXUwhKUOgurML4zvWo1djLyArFGG2mTFYDKSZ00jOTCbeEE9MWgx30u4QkRxBaEIoSZlJ9rbqudfD1ymA4Ag/lOZWKKkCVHxqn8VmYcrOKXx7+lvGtRjHT0N+qrQTo9ZeWsvYzWPZPW43vev2rpQ2HlXkWjEylU4trzicfRYRfG8PCskNf+VLzO/7DqPaZdU6zymmbjo1ggDJBotdWIe08uZU9ClmPj6TF9u8yKrzq9h0dRNal9oY0wKQkBDIClEIqEhTBeGqaMC3w5YwtNHQEmfSFFZXRJIkmvkbOXL7CMduH+NE1Akux17GJv1d68XBjeY1mjOi8QgaezSmYdWG1HOvh7/ev8D4cOC5KL45mdWOFkhNhe/3QV19tRILsCRJxGbEcin2Emeiz3A86jjbg3dhVaaCDjRiQxxtnbFaulXo9nm1Us03T36Dj6sPM/fNBGDV0FWV4lGrTI+hxJlhK+fR0kn5r0hTvN/Iwi5Tam4k3mD2/tn8evlX9Fo9n/X4jDceewNnjbP9nrximmzMWgRNV+7hUkY4726eALTjyO0jtKrRCoAhjYZgk2yExAZyz9CanKVABDTUMv/Aoqc7MrR56UQgu66IhIRViCZTcYE4LjFq22UsZHnHbg5utPdpz4wuM2jj1YbWXq3xc/MrVey7IuqXCIJADeca1HCuQa86vQCoNWMbZuEmRuVpDMpjJKt/JFm1kkRDW/688Qm96vRiy/nocodqBEHg/cffR5IkZu2fha+rL5/1/KxUNooj8FwUH24JRctjGJXHuZOcLhfvqgRkYZcpMbEZscz9ay7LzixDo9Twfpf3md55eoEbefKKXIbyECmq9ahFX1xtgzGJahbuCmH2iAksOLKA9x5/D71WT1f/ruyP2E8Pv0S2nahOosGMgPB3VkyrUv/4083phKbuw6g+g1FxFpsiFgClVBWttSVfD3mGLn5daOzRuNzeaWXVL/HROxGVXBeNtS5u1lFYhCjSlXswqv+kz5o+1HFrjjlxBApzawSEclc6fP/x94lMieTzw5/T1rstwxsPL1f/c5L9d6FTtCNDtRez4jqCpbFcvKuCkYVdpliMFiNfHf+Kzw9/jsFi4MXWL/JBtw/wcvEq9Jm8YmYWbiCgxMPyLgASEtHJRgI82+Lp7Mmai2sY12Icbg5u+Ln60dzTgY/79ilTf6NSo9gSsoUtIVs4EHEAs4MZQdKhFVuiM49AK7ZEJXlTU+/IS20rLhWxsuqX5C2jq5Z88BYm8vGAeaQq9vPattmYlB+i1bTA3fIKasm3XJUOBUHg6ye/5tzdc0zaOomONTsW+V2Xhuy/C62YtRs3U3EFB7GxXLyrgpGFXaZQJEliw5UN/GfPf4hMiWRww8HM7zWfRtUaFfus0uUAccYInGzd0Ui1cLUOxaS4ilFxDrPiOhIiXrpG1HAewPDGw1lwZAFjm4/Fw8mD8ORwOvp2tPehJOGQ2ym3+e3qb/x29TeO3zkOQH33+rzR/g3chPb8ctCRTMs/dvIWEquIrJOy1jEvjqLL6NZh7oZqpCl3kqxeQ7TDG+it43C1Di+XWGqUGtYMX0PLZS2ZsmsK60esL9d7yCZ78FPihlKsgVm4YX9dpuKQhV2mQM7GnOWtnW9xOPIwLWu0ZOWQlTxR+4kin8kWx0sZXyKponAQWpGk/gknW1ecbT1xEJsSq/kAF9tgXIQmxKv/x66wdoxoMoJfL//Ky9tfxmg1EpoQipdzlodYlKgnGBLYcGUDay+v5XDkYQACPAP45IlPGN54OI09GtvvbV6tcOEuyaENkiSRZk4jJi2G2IxYEowJJGcmk2ZKw2g1YrFZsEk2ApqmcSQsmTSjgLujK4NbNaRaVWduJGZS07UmDioHZgVe4tcTt7FJEkpBYPRjvsXWkymqjK6P3oWo5IE42rqQqPmWZPVKMhWXaKH7oEibxdGgagPe7fwuc/6aw9QOU+lQs0O57EHuwU8j+WFR3JYPwK4EKiTdURCEH4GBQKwkSc2Ku19Od3x4STAkMHPfTJafWU41x2p81vMzJrSaUKJ0whmbL2K02EhUL8XZ2gdnRUNsmnPcFpfSWLEcsJCQeZdabg2Z3rchN4zr+OvWX2wdvZXkzGQu3rvI/pv7eavDW4UW4LLYLPwR9gc/nf+JHdd3YBEtNPVoyuhmoxnVbBT13OuV+j3nzJu3kYZFcQuLcBsH3V3a1jXb89bTzemltp0TAQEXtSfmTC80Ym00Yn0cxMaoqFquYmE5ByYJiXTlHySql+PrWoejk/ZS07Vmmfucbk6n9pLatPdpz44xO8psJ29/sxyArzCo9rFxsBxfLyn3O91xJfAN8HMF2ZO5z4iSyA9nf2DG3hmkZKbw5mNv8lH3j4qtcChKIgpBwYKd18i0iIikIGJEQIXZZqWmQ0ea+B2jV50wpnSYkiu0su9mANfir2EVrfaF067+XQts50biDVacXcHK8yu5l3GP6k7VeaP9Gzzb8lla1mhZpp2byZnJHL9znKvpazBpwjALN7Ap4u3XBasDEckNqOdej561e1LTtSbeLt5Ud6pONcdq6LV6+8EZGqUGhaBAQsJis2C0GkkzpZGUmURsRizRadFEJEewaN9f2IRIUlVbQLACoBJr8vWZNvQJeJsufl1KvYibN1TTyOUp+rfpzoLTL9B9ZXcOTThU5hi5s8aZN9u/yQcHPiA0IZT6VeuXyU7e/g4N8OHTg8eYtX8b/ZpXLbdNmdxUiLBLknRQEIRaFWFL5v5z8d5FXtr+EsfvHKerf1eWPrmUZtWLnnitOr+KoLAgAjwDmNphKjEpJgCU6BFQYFSeRmOtQ3SykXmj3+XZ35/NEnYk7qbdZdGxRewI3cG8nvMK3QhjE21sv76db09/y+4bu1EKSgY0GMALAS/Qv17/UpcLiMuIY3/Efg5EHOBQ5CEux17OuqAWUIk+OIhN0djqoBH9UUt++Ln6cvSVXqVqA7JKB+jUOtx17vjjn+vayp1ZXq+EBbNwE5PyMkbFBVKVQXRbuQVfV18mBkzkpTYvlWvBslm1Tux+dje9fu7Fk2uf5PCEwyXaMFYQk1pP4qO/PuLnCz8zt8fcMvcpL9lOQ5opDa1KW2F2ZeQY+78ag8XAnANzWHRsEVV0VVg1dBXPtni2WO/32O1j/O/0//j4iY/59tS3zPlrDq6u/qSkZk35XayDSdD8FydrL/zcPHnc/3HqVKnDkcgjNK3elC+PfUmmNZPDEw5T1TG/t5acmcz3Z79n6amlRCRH4OPiw5zuc5jUehLeLt4lfn9W0cqx28cICg1i542dnL97HsjyQjv7dmZU01F08u3E3Thv5m6LyLfo+Z9+jQszXWaUgoBNkhBQ4yA1wMHaAFeGIwhGPh1j5ucLP/PxXx/z+eHPmdBqArO7zi62fnlhawSfD2/Ohqc3MHDtQF4NepVVQ1eVqc9eLl50r9WdzcGbK1TYszd5mW3mCrMpk8V9E3ZBECYDkwH8/PzuV7MyhbDv5j5e3PYi4UnhTGw1kYV9Fpa4+mFQaBDd/LvRp24f6lSpw6arm6jnf4mrwf4YLTYcpPo4iA0wOmxjbJfXicuIsx8pp9fq+bTnpwXu3LyVfIvFxxfz/dnvybBk0NW/K1/0/oIhjYaUeHt7hjmDXTd28Xvw7+y4voOkzCRUChWdfDsx94m59KrTi7bebXPbqw2Oapf7cmjD6Md8CzyQY+xjDRnTvDljmo8hLDGMRUcX8cO5H1h9cTWzu87mnU7voFKoCszeKWpj1JEZTzK762w+PvgxwxsNZ0ijIUDps4D61+vP9D+nE50WXarBtSiyd/jK9WIqngqrFfN3KGa7vHj6cJOSmcI7u9/h+3PfU9+9PssHLad7re6lsrEzbCfLTi/j91G/IwgC+2/uZ8OVDaQlt+XYFS9skoQkJNCgzmXQniMyJZIB9QewoPcClIIy34zgcuxl5h2ex7rL6xAEgdHNRjO1w1QCvAJK1J9MayZBoUGsu7yO7de3Y7Qacde5M7DBQAY1GETvOr1LVIjsflHSrJibSTd5e/fbBAYH0t6nPRMbfcVXu1LyzSzyino22bXgLTZLrnK5f1yKL/WxcsfvHKfjDx3ZNHJToRuWSjtYfHnsS6btnkbyu8kP1ffzMCPXipHJx66wXUzaNonotGimd5rOnO5zynRyUYOqDajhVIOg0CAGNBhAw2oNSctwY+/1qzhInkhYQdJzJ7IHk3o8wbPD21DdqXo+O2eizzD34Fy2hGzBSe3EW4+9xdSOU0uUxSFJEkduH2HV+VX8dvU3UkwpVHeqzviW43m66dN09e9aKUWsJEmy17Apa6ndT4Y2L1EGTO0qtfl91O9suLKBydsm8/revlS1zUZLE/s9RovNHt7JS3ZuuFqpZlGfRfRZ04cfz/3Imr0NS136oEWNFggIXIm9UqCwlyRlNC8JhgSUghIXB5diPwuZ0lEhf/mCIPwKdAeqCYJwB/hQkqQfKsK2TPlJM6Uxbfc0VpxdQROPJmwauYn2Pu1L/HxeT+zt3nVpVr0Z269vp3/9/ni7eLPn+lXMNm8UQgwZyn042XpitHiy+YSOaU/kFvVzMef48MCHbLu+Db1Wz4fdPqSubgTL9sfy+P4LeOuvF+rt3Uu/x8rzK/nh3A+EJobipHbiqSZPMbb5WHrU7lFmMTdajIQkhBCaEMqNpBscCLvKydthZFgTUSjSUGuMWEQjmdZM+zMCSnQqJzycqlDdqTo+rj7U1temYdWGtPRsSSvPVhWyKDiy6Uhae7Wm8ZLuxGpmU938IVqxhf26TZLyee55c8N71elFe5/2LDmxhMzkL4D8g1JRG5oc1Y54OntyM/lmgdfLUicnJj2GGs415FBMJVBRWTGjK8KOTMVzJPIIzwU+x82km0zvNJ2Pn/i4VGJTkCc2K/Aab/d7jKTMI8z9ay4fdv+QdLMBLc6oJE9crENQklUQLKdYBMcHM3v/bDZe3Yheq+fj7h9TRzeChX/cJtl4y35fXm9PkiQORx5m6amlbL62GYto4XG/x5n5+EyeavJUruJjJSHVlMqpqFOcjDrJ2btnOX/3PDcSb5CzWLBCckEpVUUpVUFh9UQputCshgfX75mw2gRARMKKZM0k1WrAXWPlTNQ1tgb/gUhWhpBKoaFjzcfoV68fwxsPL9GO3cKo516PVtolXMh8m1jNJ3iaFqKRsjKWkneLAAAgAElEQVRufHLE2gsLgwiCQDuPkSw9/w6ewnUcpPwbgtx0RWcZeTp7EpsRW+C1stTJCU8Kr/TDy/+tyKGYRxSLzcLcg3P59NCn+Lv5c3DCQbr4dSm1nWxPTCQdxd9ibbTYWHkonR8mfcQnBz+hydIm6DSe6DLaISDYRR2ywgHRadF8dOAjfjz3Izq1jtldZ/N2x7c5cC0jX6w3G6PFxvydl0lV7GXx8cWcv3sevVbPa+1e46W2LxUpknlnGK/18MbFLZS9N/eyLXgv4SlXAREAT0d/Ovu3ZVzzcTTxaEKDqg146afb3E3J79Heuy3gXNCalAXS7gg4CFDTZsMqxGIRwrGpQ4hOCWXmvpnM3DeTtt5tebXtq4xpPgYHlUOJ+58t0jP7deCdzZ8QoXyLOM3neJmW4KR2tF8vKp4deC6K3af9QanAoDyJgzW/sGeYrQSeiyrUjrPGmQxLRoHXylIn51r8NQbUf3jOg32UkIX9EeRm0k3GbB7D8TvHeb7V8yzptwRXB9cy2YpKziBNuZMk9Uo8zDPRiS2BLE+sUbVG/DTkJ9LMaRwMNuYTaQe1Bb9a+6j/9SAsNguvtnuVWV1n2ePtC3edLVDURQykqYK4Y9rK8cBEmno0tR/b5qh2LLK/2TOMVGsEBtVJYgynGBt0DQQbGoUDKmsj3GyjcBAboREb4mx1Y1z95rnKC9xNuVOg7YLi2NlYxKxrAgrUkidqyRNMnXBOUdNGk8TN9L1cifmTiVsn8sGBD/i4+8eMbzU+Xxii+Fh1D2b+8T5XLdMRnTfy+YCFJcreWbgrBLNFh0ZRH5PicsHvwSYVGToRBIHCki1KWycnOi2a2IxYWtZoWWzfZUqPLOyPGBuubODFbS8iILDuqXWMajaqzLZuJN4gyXE2qdIFtLaWqKR/YuU5F+bcde4M/TuBZeGuEKKSDWhcjpGg+pF1IXcZ0WQE83rOo6573Vz2807TbaSQqtpKmmo7kpCBm9Ca9WPW0qdunyIXKrM93IiUaxhUh0lXHMaqzRJntVgbV+swfB074CI0JSaj8DhwtqgWRmGLlEWRbLSA0RkXhuBsGIykuYBOuYmJWyfy4/kfWT1sda5wREli1XpFa5ysTxDNRhKMbwPFC3v2Z60R65Gh3J/rEJOC7isIo8VY4L4DKK5QWX5O3DkBQDufdsX2Xab0yML+EFARlQUzrZlM3TmVZWeW0aFmB3596tcyxy9FSWTpyaXM2DsDlCo8TVPQmHvmOM0oy5PsPG9frr4ODfChjncCrwW9xuHIw7TxaENgv9/o4teFwHNRPLd8X673mD19t5FGqmozaaptSJhwFDtSXXqGxcOH07de0Z/Dj8fOMOOPb0kW9mLR3gJJgYPYDFfzQHTiY6gkDwAyUiGDgtMCs8WsIFHNRqdW8lQbHzadiSr0nuIQEBDMraia0YEfB0cyZdcUWn/Xms2jNttTTouKVef05t2EsWQo/+LdXV9QVbeo2L+X7M9aLXojqQyIpKEk/yyuqNBJgjGhyJICxYWDcnLw1kG0Ki1tvNqU6H6Z0iEvRz9gsn+sUclGJP6ZegeeiyqxjfCkcDr90IllZ5YxvdN0Dj5/sMyiHpkSSe/VvXlz55t08+9GyBtX+N+wd6ipzwqBCGBfYszZ1zRTGm/vepvW37UmOD6YFYNWcPLFk3ZRL+g9dq7vRIZmPVHaF0hVbURna4eX6RsaqD5k8fDhhYqETbSxLWQbg34dxAu72xOn/BGFpMPd/DI1M1fhaf4MF9tAu6hDlmAVJlrZrxflrX4+PCtF8fPhzXFUl+9nE5OSyYSACZydfBZPZ0/6renH3vC9ufpSUB9zDjxqyROd2JZkYQ8Ldl4rts3pfRuiUytRkpUvLgqp+e4pKnQiSiJRqVH4uFTMpq09N/fQ2bdzkWsNMmVH9tgfMOU9Tm379e2M2zwOQRDYNnobAxsMLHNffr30K6/seAWbZGP5wOVMaj0JQRCoGZDljeWsgpizr+8F/UT6ge+ISo1icpvJfNbzs1y7WPO+RwkbsWIQX13+FYsyCXdFZ7SG0dRya1zkbCXBkMCKsyv49tS33E69jaezJ26Wp3Cy9UItFf5Z5RSsouLAORcAJUSyhjAFNfWOuWYlC3eFYChHrfNs8a7rXpdDEw7xxKonGLZ+GKdePFVkrHrq+vO57DjaOmNUniQi9Sq1Z5iKnO1lvzYj6CTxVvBwERjYxI/9wXElmilGpkRispmo717+ImARyRFcjr3M872fL7ctmYKRhf0BU9bj1ERJZO5fc/nor48I8Axg08hN1K5Su0x9SDOl8fofr/PzhZ/pWLMja4avoU6VOsX2yUYKieplGKyHaKZtxoYRG+wHZBT2nFFxhiT191gUt3GwNeXY5CB7ne/skNTU9edzCU32FvtVF1ZhtBrpUbsHi/suZnDDwXRfeKjAbIxsfAoQrPk7LxOZeh0n5xia1zGwKeIXFl+IJEJ1h3vaeGwY7JUXAWIsWhzmuIBYBVdVTawmHzSKrJK7Core4KVWCPaFVcjvFVd1rErQ2CBaLWvF2M1jOTEpK/ZcUGgua/3in/eafQqRSRGCxla32E1BQwN8sGgaM3IjrJnUqdhCbzm5cPcCQKmeKYzN1zYD2MsbyFQ8srA/YMqSJpZmSuO5wOcIDA7kuZbPsWzAsjLtIIWszUIjN44kPCmcD7t9yKyuswrd5JOzrxmKwyRqvkXEgK/yec5M/q7A+i/Zz0Wk3CRJvRyj8iQq0QsP00zquTyRS9TzZoNM3byVRad3cjRmOyqFimdbZFWIzCku2Z5sQUuaVRyz8rLfXL+fd4NCqFvzNnHmK1y0XcSsNYMVboQq8HX1xc/Njy612pKaoePSbTMZmQIuWg3+1Ry4EhOHWUzBJiSQZL2CTb0vqwFJhVZsgZPtCZxsXRDInwe+8OmWxa6f1HStyTdPfsPYzWM5HHmYoQHdChTmvN68UvJAkHRYFLfJXj4obraXlJl1eHdx5ZjzcvzOcVQKFa08W5XquYJYd3kdAZ4BZaqdL1MyZGF/wJQ2TSw8KZzBvw4mOD6YJf2W8Eb7N8q0tV2SJL478x1v7XwLD0cP9o/fX2gt9Jx9/c/mo0SxFIPqLzRiPXzEaXw5ZFChom6ymlBV2Ux05nIElOgtz+NqHYKAmh6N/8myyRmuMQu3SFH/gkF5lNvRjkzvPJ0pHabg6eyZz/7QAB+m5AlRSNgwKUIIN5/EaDuNRRcBVgi9qaWpR2umPDaFAK8AmldvTj33ekXGeTvP24erKffAK5KBSXGdTMVZDMqjJGgWkSz9hJtlFM62fghkHUrio9eVaEEx8FwU/93pgZdxOe+vszG9b8G55HkzT0BAKVXBRnKu+4qa7d1JvYNCUFDDqUaRfcrLgVsHaOvdtswORDbX4q5xKvoUX/T+olx2ZIpGFvYHTGnSxA5HHmbY+mHYRBu7xu2iZ52eZWrTYDHw0vaXWHNxDf3q9WP1sNVU1RV/2EHXRjqSXKZgMN5FbxlLI6fneLdf00KF63DkYV7c9iLB8cE42h6niuUFVFSzX98fHGf/d3SyEasQS7JqDRnK/QhocbL2QmtrztQOU6nhnCVEBZ2B6qPXcSfZgElxlQzlQQzKI4hCMkhKHMSm6C3j0dpaoJHq4ZrmzPzeJT/AuiCRVOCETgzAWWqN1TqRTMV5UlTrSdT8j3RxD9XM76KWPHmikUcBFnOTc6aiwrNE4ZTs1zvP20e00QFJyF32tqjZXnB8MLX0tUpVyz7BkMDJqJPMfHxmiZ8pjO/Pfo9KoWJci3HltiVTOLKwPwSUxKtbe2ktE7ZMoJa+FttHby/zSTbhSeEMWz+MS/cu8XH3j5nZdSaSJDFm8xg+7fFpgbH1bNx17rzefjJP1n+y0PzjwHNRzNt5nquGZaSptuOhq0l10xx0Yv60tmzRTDWlYnFeQ5R1EwCu1mEIOGBQHkansTFz30waV2vMtE7TCpydDGibwkeHX8Ui3EWQHNCJbXG0dUJna4sCpwLbLCmFhcoAREni1ryBBJ4LYMbm1iSYD5Cg/pa7Dm9Tw/QJm84oaevvXuR3W57F8+l9GzJqixVB+udnXNz5oWdjzpZ6U9DWkK2IksjghoNL9VxeMswZ/Hj+R4Y1GmYfqGUqBznd8SFHkiQ+O/QZYzePpZNvJ469cKzMor7v5j7arWhHZEokQWODmN1tNgpBwciNI9E76IsU9Ww+7P5hkaL+1uZ1nMmcRJpyBy7WQVRJ+y9eDgUfguzlpuXnCz/T4OsGRNnW4Sp1xce0nCrWiViFeLzFd1gxcDUvtXmJTdc2sfbSWiBr4Tgnzz/2GE086uNhfpuamavxML+Hk60bCpwQSbfXboGivdmCmN63YQHbeHLbGhrgQ1UnLU62bniZvkSQNMQ6fESaJZY5267Qed4+as/YQed5+/KlsZZ18Ty7Xa1DBi7qKghkzVyKKr17N/0uN5Ju0LFm/gXuolh3ZR219bXLnXO++uJqkjOTeaP9G+WyI1M8srA/xNhEG6/ueJWZ+2YytvlYdo7dWeLDMPLy7alv6bO6D17OXpx+8TT96vUDYHzgeKyilf8N/B8Ah24d4lzMOa4nXC+VfYvNwus7/kOkcjogUcP8Oe6WlzBZNAhClieZE4X6DinOMxkfOJ5a+lqcmHSCbwf8F383PyQy0GjSeKmbH0MDfGjn044Pun3AgiMLCE8KzzpbNMcOUG8Xb86/dhAnWw8UZOXbixhJUv3EPYeZ2ISsc0yL82YLYmiAD2M7+OUT97y2soVYLflQ3fwRIhkkav5HksFS5B6F7MHBSmIu+yUZgFIyU0g1J9KnYfOsmjzJRhbuCil0D8SusF0ApQrh3U65zZ83/mRs87FlLlMMWadZLTy6kPY+7ctUs0imdMjC/pCSac1k5MaRLDuzjHc7v8vqYavLtJnDJtp464+3eC3oNfrX78/RF47m2tpf370+CkFBWGIYb/7xJp8e+pT/7PkPC48stKelFcfNpJs8/tPjRNnW4mTrhZfpa7TiP5kryQYLnw9vjo9eB1iwOW/gtvoN7hpD+X7Q9xx94SiHIw8TeOtD/pzWgVvzRjK710g23Jhjt9GvXj+eavwUP1/IOi+9IJHJFkOj4jwxDlMRhTRqmD5HLfkU680WxSdDm7N4VCt89LpCPeOcQqyRauFmHYVReRyTkHuAzA6zZDO9b0MyNOtIV/1hfy3noJF3dpKT7KP+9l/WlmiD2+/Bv+Pj4lOqzJYVZ1cAMCFgQomfKYh1l9cRnhTOjM4zyjVAyJQMWdgfQtJMaQxYO4DN1zazuO9i5vWaV6Yfg8FiYPiG4fz35H+Z2mEqgaMC7cXAFhxZgNlmZlbXWXTw6cCAtQO4kXSDneN2smbYGhp7NOZczLli2wgMDiTguwCC44NpoPqAapa37F5zNhJZseQRHay41fqQO7afGdnsaYJfC2Zsi7GM3jSa43eOM7/XfHuRr6kdp1LfvT6v7njVbqe4PP06NW8BVgQUaCR/3CxjcFK78N5Ad/ZP72IX4rKcGjY0wIcjM3pwc94AjszokW+AyN7ZmY2LdSCC5ECGam8+WznDLF0b6XB1P089pyEIQBXXWEY/nkISu1lz4gqPzz9QaBjnUOShrH+Yc4fm8g4eAEnGJP4I+4MRTUaUuP55pjWT7858x4AGA0oUpisMi83CnL/m0KJGCzl3/T4hL54+ZCQZk+j/S39OR59m9bDVZc4eiDfEM3DtQE5Fn+Kb/t/wWvvX7Nde3v4yy88sJyYthsX9FvNul3epX7W+3ZOr4VyDFjVasPL8Sn47Hc7iP28Sk5KZK2PHKlqZtW8W84/Mx0loiN44HZ3WF1FpxWLLLZwSIlfTV/P2gTVU0bqz9ZmtDGo4CICfL/zMb1d+Q/wwyzONSI5Ap9JRw7kGS59cSpefurDgyAKmdJjC5djLxGbEIkpiLnHaeHUj03d9QERKML6sRyu2wCCeJFW9GYcq8fwapuZUYj061Oxg301b0eTNbvLVVyXZ1IxMxZV89+b07hccWUDj6v5sHzOKy7GXmbJzMcFp1TkareLYzbW4mSahwLnAbJk/wv5AI9YrsOZL3hj9motrMNvMjG85vsS1iVadX0VsRiw3b3an9owdZa5j9OO5HwlLDGPrM1vlQzXuExV25mlpkM88LZh4Qzy9V/fmatxV1o9Yz9BGQ8tk53bKbXqv7s2tlFv8+tSvuexM3jYZi2hhWsdpLDy6kBmdZ9DYo3Gu51MyU3hqw1P46jpx/GKnfDn2Mwf6sjr0bXbf2I1efBJX04v2zTlqhYCzVkWSwQKAjSTiNYvIVJ7H0daJprp3OPnesFztDVw7EC9nLzr5dmLF2RWoFCo6+3bm/cffJzotms8Of0aiMZE0Uxq/Pf0bHk5ZaYSRKZGMDxyPg9KBmMihhGQuxcU6ECexCybFNVJUv+Hp8BgL+03jvZ0ruGPaS13tM8ztP6JSDqrOy6DVkwi6sRbfzN9yfX7ZYRybaOOLo19wMfZi1o7fi2uY3GYyEwMm0vbz9Vwz/A9X6yAcpH9qz/vodRyZ0YPbKbfx+8oPX+XzKNJH5Gs7+z7ICuc0WdoEVwdX3m/7e4nOOzXbzNRcVJc0gxPVM7+wF4Ar7mzUvKSZ0qj/dX3qudfj0IRDchimnMhnnv4/Iy4jjp4/9yQ0MZStz2ylb72+ZbITmhBKz597kmJKYfe43Tzu/7j92uZrm0k1pbJuxDoyrZnEZcRx8NZBu7BLkkSKKYX+v/SnV+1e7DvZHaMlt+eXao3kxV0vYhPuUVf1Nta03DnhFlHCUaMi2WDBqLhMvGY+IgbczW/gbOtDrNnKjus76OTbiSq6KgBseWYLVRdU5WLsRYLGBHEv4x4Ljixgw5UNvND6BVYMWkFyZnK+c1MlSWLuE3Pp4teF2jN24KBqiCikA+AgNsbd/Dqi2Z1ZgdcwWdqgVJ8iNj25wDzxt/54C2eNM5PbTMZf71+mzz6bbI/4SnoqotqMXqcmxWjJ5/EqFUre7fIup6JOsebiGvz1/kwMmAhAQoozksaAVXEPB9s/wp7tia+6sAqA97u/yJJdqUVucNsWso2QhBB+Gf4LC3eULL1yxZkVxBnvUN08J1d539LUMQL49NCn3Mu4x9bRW2VRv4/I86KHgHhDPD1/7klYYhjbR28vs6hfib3C4z89jtFq5MD4A7lEHaCTbyd+Gf4LAFqVlrc7vs2iY4s4G3MWyFqQ1Gv1LOy9kLk95uabzmcqrnLXYTpmMZV94/dhSyt4o09UsgHBZSf3NO8jSI54mhbhYuuLVbhLjG4Sb+18i4O3DmKyZqUhKhVKLr96mZ1jd1LVsSpNPJrQ2bczx+4cA0Cj1FDdqTpXYq+w5PgS7qRm1Vr31/vbMyy89TpsQgqiYACydp+qcEcpCBgtNszCTSzCXdSSX4Ex6LsZd5l3ZB71v67PB/s/wCaWrTRvzkqWNiENheSEySqyeFSrXLH5NFMaJ6NOEpsRSzufdizpv4SFvRfa7Ti6XsEmpOJk65bLvrdeh8VmYdnpZfSq04uXu3SyL0wXtLArSRJzD86lTpU6jGw6skTplammVOb8NQcHWzO0Yusi7y2K4Phgvjz2JeNbji/VGbsy5Uf22B8wScYk+qzuQ2hiKNtHby9xKlreOOnIjhKfnhyNSqFi//j9ucIrO8N24unsiV6rR6lQYrFZUCqU9KrTi5FNR3Iu5hytvVpjFa2oFKpcYpm9OcegOE6cZj4qyYMW2vl08euCtz5/tUcJKyanFdyz7sBZeowqprdR4ISEhFKdyIQW79Cyphu7b+ymulN1e9Gwmq417TaMFiO7w3fTqWYn+2s7ru9gfOB43HXu+Ln54eXshVKRtVhpE21M79uQV38PIEGxFTfr8KyDptVKUqxhJGvWYBMScbUOtR8Wklec1o9Yz+2U28zcN5O5B+cSnRbN94O/L9F3kZOcG44sQiRq0btAL3fs5rHYJBtXYq8wqfUkZnWdhZ+bH5C1aKlz30216Kdy2c72xKdtX0pUWhSW+En2mvjZYZe8bLq2iTMxZ/hpyE+oFKoS1Sb65OAnxBniaKGdQ4q58OyjopAkiVd2vIKTxon5veYXe79MxSJ77A+QdHM6/X/pz5W4KwSOCiyVqOesb34zJYRp+5/CJio48PyBXKI+e99s3tn9Dj9f+Jkeq3qwN3wvaqXavojVsGpDlpxYQqIxMV/xr+xMj3TlXuI0n6GRalNL/JLZ/Z7IdT0bEQMJDh9zT9zBe13eY9WQ3/DVV0MAauodmTdwMF8PnsbLbV/mTqKVkauWUvO95faMD5PVxIk7J2i3oh119HWY2nGq3bavmy9HJh5haoepHL19lPCkcPs1pULJ0AAf3ujaiSqqethIsHuublondLbWeJkW5/J+Czq42dfNl1VDVzGj8wx+OPcD+27uK9H3kZPsAUPEiElxHQexca7XAZafWY6ExI4xO9jyzBaCQoM4eOug/bpWpeXP8b+xdNir+Txxq2hh2bkFqMU6aMW2RaY3mqwm3t3zLk09mvJsi2eB/N8Z5A7dXI27yuLji5nYaiJz+g8u8t6i+OHcDxyIOMD8XvPlXaYPANljf0CYrCaGrR/G6ejTbBy5sVThl9xeYTSxDrMABf62+TSo2gDI8pjCEsP4M/xPDk44iLvOnQ41O/DKjleY32s+wxpnLWA+2/JZtoRsYf3l9bzS7pVc7QwN8GFXxBqWXVyM1taKlrpPmNGvVa7a5Nn9uZ18l0THjzASzg+DfmBiwEQkSWJ4a9989V0Cz0Vx5XonkliNRnGWO8nV/457N6dGNZGFvRfSv35/+/sQBIEGVRugVWlx07ox/c/pnI4+jb/eH41SY7+nZ2NvtkcmcfD5sXZvfs42H1xsuWPzAIWFewVBIEA/CRVLGfLj57RwolSZINkesUF5HAQrOvEx4J+BRJIktl3fxmvtXvt71pVASFpLnvp5DisG/syglp5sv76dwQ0HMzSgSr5263z6BhYhBg/zh/bYd2Fx7y+OfkF4Ujh/Pvun/fMoqjaRKIlM3jYZVwdX5vWaZ1+kLu3pXrdTbjNt9zS61+rOpNaTSvS5yVQssrA/AERJ5LnA59gTvoeVQ1aWOvsl2/uzEs89zSwkrNQwzSMp858CW4IgUKdKHVrUaEFwfDDtfdozsulIHNWOvLjtRXRqnX336Zd9v8TPzS9feKdFw1MsuziDAfUHsHHkRrQqbb6+DA3wITHzLq//OYFM8R6N1HNxpy9rLq4hJi2GPnX70MSjCWql2i7AC3YGY7VUw0nRDYPyKAaOESvsZdYfoxnfTeRy3GUiUyJ5qe1L9gEhu21PZ0+6+Hbh6O2jNPFoQkvPlvbzO9t5tyPBkMCl2Ev21M3kv7Nz8pJksOQ72g+yBp0Pt4SiFPyxCDFZ5YPXn2fK+vMF1nbPy/S+DXnnt/OkqbajEr1wEJsAkGG2EnguioEta/BB1w+4EqlmflBWdoozfYm1HOO9zZfYEPIVam1sgfnecRlx3LKsRCu2RCfmTozIG1oKTQjlk0OfMKLJCHrV6ZXvOyvoPSw9uZQjt4+wcshKu6iX5rg7yPrbnrh1IjbRxveDvi9VemNFHBEpk4UcinkATNs1jQ1XNrCg1wLGtxpf6ue99TpspBPr8AGikEZ10xw0kl++2Kcoiei1egKDA+2vDWwwkCX9lvD1ya9JyUwBsIt6zvBOSNp2ll2cgc7WjoRbr7PzUkKBffnx2Fle3jWETDGO6uY5GNJa8ELgVGbt+RSDxcCMvTNYfHwx8YZ4BEFAlERiUjIB0ImtEVCSoP4vKqkq9zKi2XZ9G8+1eI61l9cy//B8IpIjgCxPNzs196kmT5FuSSciOcJ+ZBtkDWanXjyVa2dlUfHggsIY2bMhUciwH6JR0FGAhTE0wAccLmFWhPxdnjjrJ2axSSzcFYJKoSLAK4DvDsRitNiQsCKgRiXVIFbcxvbrO/msx2cF2p66ayqSkEkVy0v5DqLO+T5too2JWyfioHRgSb8lhfY1JyHxIby751361+vPcy2fK9EzBfHfE/9lT/geFvVZlO/w8qKoiCMiZf6hQoRdEIR+giCECIIQJgjCjIqw+ajy9Ymv+erEV7zZ/k2md55e5L2B56IKLCA1pVctErSfYhGi8TDPwkGqny/2KUkSaqWamY/P5EzMGd7e9Tbp5qxUwKcaP4WzxjlXeCRneMegOEGCeglaW0s8zO8Rk2Ir8EeWYEjg9T+HYyWB6uY5aMVmSFgwiUl4mD7mw+4fMr3TdBKNiSw7vQwAhaDAW69DQsQi3MagOIG75TWqWt5E0p7lzcfepGednnzR+wvSzemsu7wOyBLt7IGhmmM1hjYcyrwj8/D8wpP5R/5ZnHNxcMnVx4JiyjnJmyETnWzERhIW4RYaMX+xtYIyanJiFa1Eit+hFKvjbMsdXotMvoPRYkSlUHE3JWsmIfw9aXYQG5Go/h9Kcwt8XPN7qVuCt/DLpV94usHruKly78DN+91/eexLDkceZkm/JXi7eBfa12zMNjNjN49Fp9bx/eDvy5yWeDbmLO/ueZfBDQczuc3kUj1bVJVLmdJTbmEXBEEJLAX6A02A0YIgNCmv3UeRoNAgpuyawpCGQ/iy75dF3luYB/P72Ttsu/0RRuES9dX/wVFsaV9Ya+SbxqV7WTna2T9ON60bW57ZQnhSONN3T+fLY1/yyo5XSDAk2MsLwD9TeZMQTLxmPhqpLh7mWQhkHaCR90dmsBgYsHYARjGa6uYP0P4dchBQIwkGQjM2AtCjdg961O7BvfR7bA3ZCmSLrQKV5ImXaQnOtifQqZUMadyd3Td2A9DOpx3tfNpxM+mmvSZKln2B2IxYZu2fhSiJrBuxjm+e/KbQz3FogE+OOjUFE51stA+iEpCq2g6CmC/VMO9nVRCLji7CoojA3TIp14lKJiGYFMf5/M9M56AAACAASURBVHb1N0LiQ/Byy30wiZOtJ862J2ns9Hw+mzFpMby47UVaebZi9cj5RaY3no4+zcx9MxneeHiJPe8Ze2ZwJuYM3w/6vkQDQUGkZKYwauMoPBw9+HHwj6UeHMpT5VImPxURY28PhEmSFA4gCMI6YAhwtQJsPzJci7vGMxufoWWNlvwy/Bf7YlZhFObBTAn6iEjbaj7u/jGzu822X/vh7A+M2bQUtVJNB58OWE01OXctgJiUrEOOp/T+GpP6CHfT7+KoduTP/2PvvKOjKNs+fM3WbHpCGgmBJHRCixB6710UgggiRQQFRfETBQTFgqIUBUUE9AURpPcuRXqHUEMnBEgIKaRns3W+P2JCym6ygSDFuc7xHMlOeWZ25zf3cz93GbAj37F9XTVEpUQRp/4KueiOl25SoX6euREfopkBawdwLPoYAcJERHPtfNs5G1/CqNnGgVsHaFa+GfV963M8+jjRqdEsPX6Fj7dPwWRshJ1QDpOozPVd+3q5M+fEHI5HHyfUL5QanjU4euco0anR1PWpS3xGPG4aN9RyNT92/pFWAa1suvc5fmJLzbghe2EzJxvTIESTpliLvbE5SrGchaNZd++E3w1n4t8TaejTieQ7zcgyPyjgla5ajb+bI8ejjxN+N5wWdYJZdViF0ZDT4ESGu2E4mXqRdeEPOigZzUb6r+lPuj6dJS8vQSVXWfV7J2mT6LOyDz6OPszvPt8mcV17cS3fH/mekaEjcxfUS4ooigxeP5jIpEj2DNpDGfvim7YU5GFaREpYpzRcMX7A7Tz/vvPP3yT+ISUrhReXvYhGqWF93/U4qBysbptjOVr6kWtlx7ll/B99a/ZlQosJuX9P06Wx+NxilvdezoHBB5AZK7E0/AAXMxZjJrts7KfrLuNoas2HTT7kh04/FHroR7UtT4L6K0QMeOk/Q45LofPnPGRf7P2CNRfXMCj4UxS6hoW2sxcq0r16MxadWcSd1Du4a9yp7lmdpWe288WGGxgzXkAp+mESxVw3Qs8QP2p61cSQ5c2LC74jcOxmBs67xd/XT5NpyOR49HHmnpxLSlYKLnYuNot6wXtqqfyuIGS/NM1kkaD6DgEVbobsaI7iyvXmkJiZSO+VvfFy8GLTgD+Y8nLtXKvax0XGWw0GcmDoVia2nIi/iz/Rur2EVD+JWnOLNPkW4lVfICAjWWvI5/b6ZNcn/H3zb37u+jM1PK1PhE1mE6+tfY07qXdY3nu5TeWdL8ZfZOC6gYT6hjK9w/Rit7fGtwe/Ze2ltXzX/ruHLslbXBimRMkoDYvdkllQqACNIAjDgGEA5cuXL4XTPhvkWLeRyZHsfn03/i7+Vrct2NA5LwYhlgTVNBxkFfmtx2+FhNlgMhCXEUflMpU5fL4SSkMSWvkpMuUHcTC14r7pGJO2RtMz5A2L594WMxm9EEk1xWQys/wRyP8l5jxk265t4/O9nzOwzkAuXWyOwZxV6FhOKgcmdxzOnBNzGLB2AAtfXMjaS2u5FqtAaTCg4oGPOG+o3l/nkzh0PohkYTd28g2Yk7uSqE3k41VXMWs1+Lk2oaZTFj1Dir7nRd1TEXKvLWemkN0M20CC6lv0QiSe+okoKIMAfP9K3WIjNfQmPWErw7iTeoe9g/ZmrwGE5C9ZkFOaQaPU8EHjD7gYf5Fl55ex7/oGkpWHKKN/p9A9yZDv4btD3/FWvbcYVHdQkdf5ye5P2HJ1Cz93+Tk36asokrRJucbG6j6rH6okNGS7F8fvGk/fmn0Z3Wh08TtYoSQtIiWKpzSE/Q6QV63KATEFNxJFcR4wD7KLgJXCeZ8Jph2axsYrG5nZaWahFP+CWHK/AP+IzhRAYFqb33NL2+bgpHZiYJ2BzDgyAzeNG/dSzKipiVGIQys7g8bUGIMQQ3LqA5dJ3tAyhdMBrhkX8mmLT/m89bhCn+c8ZE2qKKn58+vU9KrJnK5zqHHEcgJPitZAWaeyfNH6Cz7a8RGT909GFEVU6ZZreue4eKZuv4zZ4IeL0Jc0xSZiFCPQmOtj0tVEQLDaD7SoMDlL9zRH1HOyNadsO8NZ7ddo5cdx14/A3pzdIcq3QDPqCevO8X8rzvD+8tPIBYFXG/rzeY8aDFg7gL9v/s0fL/1Bo3KWu0XlNIHOCfms7lmdz1t/zvTdbVAKAdibm+Tb/kbqcYZs+JRWAa2Y2bnoyJYF4Qv49uC3DK83nLfqv2Vxm7z3yMdFSabzl9xMvsnugUUbG0VxIe4CfVf1pa5PXX7t/vCLrjmUNLRSwjqlIezHgcqCIAQC0UBfoF8pHPeZ59DtQ4zfNZ6wGmE2tQOztlCUpFyIXnaNsaG/8lazJha3eaXmKyRqE/np2E+4ONclOdUPJ1NnMuR7MZOBs6l77gJiXivWKMQRZZiJhprUdnlgzVt6yHqv6E2qLrtOjEapsckv+l377zCajWw6c4+Dx04Xnsrl2T7n+tViVVSGiogYCvn5CybjFLTIC4p/cYtyt1Nuk2g/Hq3uLO76ETiZugCF3QAT1p1j8ZFbuf82iSJ/HIlkw63xnEvaxLT200pUYjmn9LCzugxk5Pdt64WbxKu/orJbEGv6rEElV1k5SnZXpGGbhtE+qD0/dv7RorjmvUciIucyp5GhP8C7db9/aNdJbHosXf/sioPKoVj3osS/zyP72EVRNALvANuBi8AKURQLF6H+j5GSlUL/Nf0p71Le5oUsSwtFWtlp0hTrGRk6km+6WHajADirnRlYZyCBroHIXP/EoNpPqnwjoqBFhl0+ocqxYkVEEpU/AuCuG82Mv65ZPf6GyxtYfXE1k1pNoqZXdnckW/2iCpmCqdsvWxR14Z/jFLx+AUUhUc8hr1gXFyZnbfHN11XD+kvrCZkbwr3MG4xv+D+qOfWy2iFp6dHb+fYXMZCgnMa5pE24Gl5jzb6QQuGg1+9f50TMCa4kXsktgZATspmTuDOz83e4KB6EVWZnEk/Exc6Bbf235VbAtMTRO0fptaIXwZ7BrOqzCqW8cJmEgvcoRbGEDMUOXAyvcvJibYvbF0eGPoPuS7sTnxnPxlc3PrTFL/H4KJXMU1EUtwBbSuNYzwvvbn2X2ym3OTDkAC52hRciLTGmY9V81md238wfKKMO5MSZrgTuK7rZQVmnsrzT4B2qeVTju32/cjlWh2fmx7hrXBAEGL38NFO3X861sjPke8iSh+OufxuF6G3VutUZdYzePppgz2D+r/H/5f7dkl+0dTVP3t/8BcNXlqWSc4vcsVo7tpjnOAWv3xp5xbo4i9zSMZXKFOQe8+m5fD0hPiEs670suxRDZ+vnNOXpW2Amg3jV12TJz+BqGIKL8WWik7WMWXkm975cTbzK0I1DMZgM1PKqhVwmp7pHdcKCw/Bx9CFNl8a1+9cIqxeCUqZi6vbLRKVEkmA3AQeVwP4hu4ssH3z23lk6L+mMt6M3W/tvzRe6au1epMo3kKJchoOxPS7Gfg8VSmgwGQhbGcapu6dY98o66vsWWxpc4gkglRQoZdaFRzN2y69cNv5BOfnrxMb7Z6862EBBodQ7LMJkvo9jxgRiDdmhc9b8zDlolBq6V+1Ol8pdEASBDafvFnJVCIAJLcnKBajMlXE0ZSuaNet2/qn53Ei6wbb+2wpZhXldNuvCo/lozUGi5AtwlLcnOjk0Nx1fLgj5xDGHvPHlPUP8OBF1n8VHz2EgEzVlQYS8XT8LzgiKcwflvad3kpPAcQvRwgpuxeqZ1HIS45qPY8vZeAbP313kol3O+A1CNPGqrzAIMZTRj8bR9KBwm8EsMmnDBXqG+DFp7yQ6V+rM2GZjORN7hiuJVzgec5zZx2Yzrvk4Nl7ZiJPKiZCyIfQM8aNG+QzaLhqIo8HIhAbLePO3WGKSIy2O50LcBdotaoeDyoFdr++irFPZ3Ptvaa3B11XD5bSNJKnmoTE1oozhHQSEEocSmkUzg9cPZuu1rczvPj+3C5bE04ck7KVItrAd4rr8B1RiRWTal4sUYUvkCOXBWwdptmAzvvIw0FbKt40tzQ5y4uStLR6mKdZiEu7jqRuPgMxqaJnepGfKgSm0qNCCzNRgmk6xLoBTt18m0bwXFAacjJ1yzwVYFPWcc+YIUs5LJ171M1myC5TLWoBKrsJZpbDYqAIsW+QFr6VFNQ0X04/yw9EfiMuIo0fVHkxrP43KZSoX66PP4dWG/sw7tpIE1QwE5Hjrv8TOXNiVkazNziht6NeQVF0qAHV86hDsFUyAawAzj87k5+M/82GTD3P3OXvvLB3+6IBZNDOxwTLm7jKhNegtjufsvbO0W9QOhUzBrtd3EeAaABS91tAwOIJDJ2dhZwrBU/9xbknjnHtkS40WURQZtXUUS84tYXKbyVJxr6ccSdhLkanbLxPDPMykUUb/BQKKEnecgeyklBFbRuDv7I9w7xWL2xScRsemxzLv5Dw+aPwBjipHq9sBmEgnRbEOd1lz7MRqRbp31lxcQ3RaNINrfM34tecLCceJqPv8fSmemH8yZLWqEyjMZVGKRTeedtUomdQjGKBQOKKjsTOZ6oPcV/6Cu2EkXmo7Tn/WweJxrIXJda/jw9+Rf/P7md9ZfmE5WcYsOlXqxMQWE2ni/2ABuigffc6xdUYdmZoFxKu/R2WuiId+HErRp8jr61SpE4PXD+a+9j5DXxhKDc8ahPqF8l377xi8fjCv1X4NH0cf9kXto8fSHjiqHNkxYAdDf7ubK+oFx1PO+y4dF3dEo9Cwe+Du3EqeRV3HR1t+5rppCjU9GuKQNoF7ejHf923Li00URT7e+TGzj89mTJMxjGs2rshrl3jySMJeitxIPU6GeifOhjBU4oOu7iX1Zf566lfO3jvLqrBVzNjgZlNG3uR9k/nl5C+8WvNVKpepnG+7gvunKzYjCpn8PewnansXvYD2W/hvBLoGsivcF61Bl+8zrcHEkiO38i2K6mRX0JjqFypSVRAHtSI3G7SgIGnMdXE2hJGqXIlBiEaX2g9RbG11ATpHgCZvO8TVtP0M3zSdIdtPkKSLw0nlxOu1X2dkg5EWr7U4H/2Z2DMMXDeQM/fO0ClgIDeuvYxOtJ417KrJXhStUqYKi3ouYvHZxUw/NJ1At0BerfkqJ2JOEJsei4+jD8vOL2PguoEEuQWxrf82KrhWICb5hsXjXk89Suvfv8bD3oNdr+8iyC0o3+eWriNdvotEww+0DGjB5n6bLUauFPdiE0WRCbsnMPXQVEbUH8G37b6VWtw9A0jCXkoYzUZS7eYiN3nhYsxvZZfEl5muT+ezPZ/RvHxzXq7+MnJdTLGuhujUaOadmsegOoPyiToUdlWImEhXbCHEs2Wxop6YmcjuyN2MbTqWP3foLG6TV9TNZGEWklGKxdcbyREia8LqanwdpViWJOVC7qnHU3b6TBqWa0hFt4q4a9yRCTIyDZncS7/H8duXuRAfgVFIBBUIJnscjfX4v9BJfNFxYG7cvyWXgzUfvY+LnFeWjmbllZ8QREeqKb/i7s1QdAbLZYBFRNLlW9Fr9pKhb4GDyoGK7hV5r9F7HLp9iD0399BxcUdaB7Tmx04/8uXeL/l0z6c0L9+cdX3X5WaKWhpPhnw/iaoZ1HCpwvbXtlssElZwvzT5Ju6rfsFFqMeW/lsK5T4U/B4s/T1H1L8+8DVvvvAmP3axHE4p8fQhCXspMe/kPDLFSPzECch4ULdcIHt6a6n2tyVmHplJXEYc6/uuRxAEmzLyZh6didFsZFzzwlPkgvtrnM5iNCbyWZuiswTXhUfz8Za5mEUzG4+WxdVeSZKV2uY5iGSLvyBqcq/dWiZazsvOmrAKCDiaOlBG1obOoVEkmrJrrOy6sYsMQwaQXSnS096TjExX1KbaOIlBqE01UImVEJBz+LwG+24PRN2Sy6FXPT9Wn4zO9+I0q05zhfkcuRKFg7EVboZhaLOc0WL5+s2kk6icTaZiP65ZoehNehzIto5d7VzpUrkLXSp3YXKbyaTr0xm+aTgrI1YyoPYA5nefny/rM++LWEQkVbGWZOX/qOYeyr7B26yWCsjZL9NgJEWxjBTlEhzNjZjXfbFVUS/q/pd1seOjHR8x7fA03nzhTX7p9kuJaqtLPFkkYS8FUrJS+GzPZ7QKaMWoWsOZ9teV3IXAgrW8wfpCapoujRlHZtCtSrd8GYxFZeRlGjKZf2o+var3KjQ9t7T/q6sXE3+9DF0qd7G47brwaD7feIGkTAP3lWcR5GpSUv1RyYwo5QIG0wOpLijcwj8vNFHIzE3Xn7ThQu6CYg5KuZA747C0+Fkw5b9nSP6mEwaTAbNoRiVXIQgCgWM3W3yB2BLvvvjILVw1SuyUMuK1kWTaLyLJfAg7gx9eui/QWGjmnJcs2VkSlN9jEhJxNQzE2diLvZcy6RlSOP48MjmSXit6EREfwXftvuPDJh8WsoBzvqdvt53nfOb3pCu208S3GzsHrcjNXrVEzxA/TKKJkZvfJcW8AU9Ze+Z0m0+vetZDJsHy/bdTCrj6/sG0w78zMnQkszrPkkT9GUMS9lJgxuEZJGQmMK39NOr5luOlF8pZLORV3ELq/FPzua+9z4TmEyx+bolVEatIzkpmZOjIYrc1mo1svbqVXtV7WUxmKWjVGoQ7KMVyCCgwmEVcNUoc1Ip8Met5szFlqJGbPdELkcQkax/Ep688g8GcR3rz/O/D1AgpOHZbMmCLWudI0N4lQ72cVM1fOCjsmdJ8CnM2VQUsJ/xAttspWbmINPlGFKIPPrqpqMXsl5WlF/iKCysYumEoKrmKbf230b5ie6vHblpFhfrMN6RH7WV8s/F82ebLYoU1Q5/BH1dGcc+8gY+afMSUdlNscpsUvP8+LkrUXnPZenMNY5qMkXzqzyiSsD8iiZmJfH/ke3pV70U933q5fy9pfWmT2cSso7NoUaEFDcsVrphojT/O/kGQWxAtKrQodttTd0+RokvJbYlXkIJWrUm4j0L0zP13itZQKDpl05m7+SxyO3NdMuUH8LZ/cMx8ok7+eG949BohtoQ8WhJ/oxBHimI16fLtAPgI3Tkzai5eDl5sOGC5wiZkZwPfV/6EURaLk7ErrobB+dxveV/gmYZMRm8bzbxT82hUrhHLey+nvIv1IngnY07y8oqXicuIY/FLi+lfu3+x1x+TFkOPpT0Ijw3nx84/8k6Dd4rdJy859z/TkEmflX3YfHUzk9tMZlyzcaw/HSMV5noGkeZXNmCtkxFk+7fT9GlMajUp3z5FpbJbYuu1rUSlRDGqwSibx1N+7FJ23thNiEdXm6yqo3eOAuQL98tLwZeOiB5BfOD/tTT2ST2C85UVcDJ2QhS0VAzaa/GYOSRrDaXW9ixvMw1rJQHylj/QCddIUE4jWj2UdPl2HE1t8dPNxS5jKF4OXoW2z8HIfeKVU3Obh1diKu6Gt/OJeg4xyVpOxpyk3rx6zDs1j4+afMS+Qfusirooivx66lea/q8poiiyf/B+m0T91N1TNJjfgEsJl1jfd32JRT2HhMwE2i5qy9ZrW/ml6y+Mbz6e9adjpHZ1zyjPrcVeWo1xi4rzbRfswk/HfqJntZ659VNysMWKzDvO05mTUcrdELX1KIq849HKwwEzJy4G5WvOYI0L8Rdw17hb7ZJT0KoVUCMKWVbHDoWn8kEudQl078qqqzMZdaeXVTdJzj6lZf0VZ/V3qOnGntuX+d/peaSJEQiiBidTd5wNL6Eguwm4i+aB6yUnC3bJkVuYMZCq2ECKYhkiBlwMfXEx9sGICj8L1ydixOy4lka/LcHbwZudA3bSNqgt1kjXpzNi8wj+OPsH7YPas+TlJbnNpIti2fllDFk/BE8HTw4OOUgdnzrF7mOJ6/ev03lJZ26n3mZl2Eperv4yYFuM/7+B1OS65DyXwm5rNqEtFPXjvmOIICkriY+afFRov6J8xwUzLU2kk2l3AidjVyauu4RCprQ6zrzjyZKdRSY6IBqCbHrYbqXcIsA1wKp1P6ZjVcasOpO7QKoQy2AU4gDoVc92d8lbtb/h82MX6fJnF8aELuCXHZbjvh932zOzaObArQMsObuE5ReWk6JLoUqZKjglDkee1QYZ+eO6C96W3RfjSJcdIFn5O0bZXTSmUNwMQ1GK2fch5zvN+1vTC9e5r56JznSD/rX682PnH4ss5BV+N5y+q/tyNfEqk1pOYkKLCcV21zKajYzbOY5ph6fRrHwzVoWtwtvR+yHuUHYF0heXvYgoiuwcsJOm5ZvmfvY0tKsrzWf5v8RzKeylaWlY+xFHJ2cy+/hsGvg1sNrYwJIVaanxQ6b8GAhGHIwt0IpFjzPveHSyy6jM1RCQ5/u7NQsnKSuJMhrrbct6hvjli2JRmSuhVZzETAZ/X4q3uI+lB++bzdGM6fgH0069zqeHeuOheQ2ltke+HqDweNqe6U169kftZ/3l9ay+uJqYtBjslfb0qt6LwXUH0yqgFUHjtliMokn+J5xTFEV2Re7iZNYI9OqrKM0V8NJ9jsb8YDaVt/MTwJRtp7mY8T9SletwU3uwrOdaelbraXWcZtHMjMMzGL9rPJ4OnuweuNumrlCx6bG8uvpV9tzcw4j6I/i+0/dFlvUtij/P/cmQ9UPwd/FnS78thXIgnoZ2dU/LrOFZ47kU9tK0NKz9uB2dr3Eh4RILXlxQouNZ/KHKjiMX3VCJlYsdZ854RIwYhDtoTPVz/w5FWzgms6lYazAl30LoC6QIS8mUHyEm2bIrwdqD98eBLI69d4xhG4ex+uIClHZbcDT0xNHUGhmOpdb2zGQ2cS7uHHtv7mVX5C723NxDmj4NO4UdnSp1ok+NPnSv2j1fmYWiYrd3R+7m872fsy9qHyqZF2X07+FgaoPAg/smF4RcH74oigiaE8Rq3iNVH8XQkKF81/67Iq30m8k3GbRuEHuj9vJStZeY332+TX1C99zcw6urXyUlK4Xfe/5uc7PqgpjMJib+PZFvDnxDywotWd1ntcXz2+pOfJw8DbOGZ5HnUthLw9Io6C4p2CbO2+cwt+45EVYjzOq+lnyChRcozWTJz6AxhSL8s5Zd1DhzHrZUYywIRpSir8Va63nJsXAcyjqQpksr8rrz3ju1uSoKsy9pik1UcexqcfuiHjx3jTur+qxi+7XtjNoynitJc0kSf8NV/gKtq3fCs4wTqTqnIkvO5iCKInEZcVxPus6lhEucu3eO8NhwTt49Sbo+HYAgtyD61epHl8pdaBfUzmpiTuFsXDMm1UkSHTbSdtEpfJ18+bHzj3jLuvDp+itoTfmFLUfULydc5v3t77Pt2jaCPYPZN2ifxS5ZD35LmciddhEjzkcpl/Fbj98YXHdwsQvfJrOJr/Z9xRf7vqCye2X+eu0vannXKvaeWSKnT8Dmq5sZ9sIwfuzyo1WL/2loV/c0zBqeRZ5LYX9US6O4PpnvtavAmzu30btG70L1N4rzCRb8oRqFaMxCKnbmYJvGmfNQfbr1KjEG8HIoy9eda1l9ceQQk6ylaRU/9t/aX+S15713AjJcjGEkqmYSGnweKGy1W3vwRMiTbduRy6M6cjLmJH+e+5NNVzex8MIXLLzwBQAe9h74OfnhrnHHQeWAQqbAZDahNWpJyUohITOBmLQYdKYHZQ00Cg21vWszqM4gGpVrRLPyzYqsX56XvO6Tq+lb0Ko3ohVvEyAGMLvLbIaEDEEtVyMIAkq5upCwNa9qx/vb3mf28dnYK+2Z0WEG7zR4p8jcgFTjbRJVP6EznsXeXJdprX9hSEjxYa23Um7x2prX2H9rPwNqD+Dnrj/nm32UhIj4CF5a/hI3km4wu8ts3q7/drEvlSfdru5pmDU8izyXwv6olkZxfTI3XdlEqi6VPsF9bNo3r0+w4A9VJ8vuWqQyV8mTaVn0OHuG+KFxqkKnJTD/teY0Lf9g+6IsnGDPYJacW0KSNsmqq6Dgvavi2I0kh4P8HvEZI5t2zldREIpujlHwpVbPtx71fOsxveN07qbd5XjMcSLiI4hMiuRu+l3ua++TnJqMSTQhE2RoFBrcNe7Yy/zRpdUnS++Gl30FRrVowbCmjYt1K1njUsIl9t6byyVhASmqFOr51OP/Gn9LWHAYCpmCiPgIKrpVRK1QFxK283HnqTirGWn6NIaGDOXLNl/mhkhC4dlauk5LrLiCFPUyQIG7/h0cTR35fX8Gw5paGFwelp5bytub38Ykmh7J9QLZCVJvbHgDe6U9u17fZVPew9PA0zBreBZ5LoUdHs3SKM6vt/7SepzVzrQJbFPifQv+UO00McjNCqK+Gma1tZklxH+cQwUzEouycMq4Zx9/d+RuetXoZfXYBe/dzeRKhM4PpdPiTuwZtCdfLHbe67H0QrG20FXWqSw9qvagR9UeRV5njsWrNJhQAto0mPVXOmUdY0v0/abp0lgVsYoFpxew/9Z+lDIlvWr04p3Qd2ji3wRBEFgVsYrR20cT4BpA43KNea/he/g5++U2oAao5lGNfrX6MSJ0RKEQ14Kzteupx7ivnINBeQt7UxPc9MNRkO3LLspHnJiZyMgtI1l+YTmNyzVm8cuLrZaLKA69Sc+Yv8Yw69gsGpdrzMqwlRaLiD3NPOlZw7OIlKBkgaKSi0RRZNv1bbQPam/RN2lLYlLPED8Ojm1D5JSuNK1mItAtoESiDuT6j3MKYuU9trVkncb+jfG092Tp+aUlOleAawBb+m3hvvY+jX5txJE7Rwqd8+DYNlYL9eYUQXuYxJbiepoWhc6oY/2l9by6+lW8p3kzZMMQYtNjmdJ2CrdH32bhiwtp4NcAQRDI0Gew5+YeFr+0mP2D92MwGZh2aBoGkyGfu0IhU/Bz158LiXresRpJIF45lXvqcZjJwlM3EU/9+FxRB+u/kw2XN1BzTk1WX1zNl62/ZN/gfQ8t6pFJkTT7XzNmHZvFew3fY8+gPc+cqEs8HJKwW6CoJs3Xk65zJ/UObQMtR4nY2uA5h5i0GMo529g7s9JFqwAAIABJREFULw8+jtmNHu6m3S30Wd4Xx8GxbXKtHYVMwcA6A1l3aR03k2+W6HyhfqEcGHIAO4Udzf7XjAm7J6A15Lc6i1rQetisxZJGRaRkpbDiwgr6re6H51RPei7vyV/X/2JgnYEcHHKQy+9cxk1oSbUZ3XD+shYB37zGuvBoHFQObL++Pfe7eKv+WyRoE9h2bRuQvXhbHHeSk0lWLCPG7i0y5YdwMfTFV/cz9ub8vnRLv4f4jHj6re7Hi8texNvBm+NvHmdCiwkoZA83qV4VsYqQuSFcSbzC6j6r+aHTDw8dFinx7CEJuwWKsnoP3z4MYDH6obh9LZGclYybnfXQOGtUcKmAXJBzObF4yzUv7zd6H4VMwSe7PwGy3QchX/xFwNjNBIzdTN3P/7IqvjW9anJq+Cn61erH5P2TqfRjJX469hMZ+uxZg6WXWl5stbTzUtwMyGg2cvTOUb7e/zUtF7bEY6oHr6x6hR03dtAnuA9b+28l9v9imdNtDk38m7D+dAyfbJ+DqK9CWd333NdfZdjaifx57BIdK3Zk45WNAPi7+BPqG5or7EUtMppFM3+c+YNYzdukKBejMb+Ar24OrsbXkGGHq0Zp9fcgiiKLzy6m+uzqrIpYxaSWkzj25jHq+tQt0X3KIUOfwbCNwwhbGUZVj6qEDw/PzSSV+O/w3PrYHxVrfr3jMcdxUDpQ3aN6kfvCAz96jphZOp7OqMtXj9tW1Ao1Nb1qcjT6aIn283P246OmH/Hlvi8J0LRnxQGvfKV4k7UGxqw8Y3W8rnauLHppEUNfGMonuz/h3a3vMmH3BF4JfoWw4DC+6FmVH3ZEWi0jUNL444JrBiZSQHWD8gFJdFz8LYduH8oNdwx0DsZbCMOkq0ugKoR2ZQOIiN9IkjaJXjV6oZKrmLr9Mplcx07MTjZyMfYjU36Az3cs5bte7VlybgnvN3oftVxNLa9anLt3jlRdqsWQTFEU2X59O+N2jeN07GkqutTGkPh/CIbg3G00SjmTegRbvJdXE68yYssIdt7YSaNyjfi1+68EewUX2q4kzD05l19P/crHTT/my9ZfltjFJ/F8IAl7CTl77yy1vGsVGZFRkjRouUyOyVw4osQWWgW0Yu7JuWToMyy2PbPGJ80/YeOVjXx77F28zdNQkt8VZDCLxWb2tajQgn2D9nH4zmHmnJjD4nOLmXdqHo4qR5r6N8Vs9CEr0x+l6I9C9MrNOrUl/jjLmEVMWgw3k28Sb75O1aon2RsZTprxBiZZAgDLLwvU9KrJgNoDaBXQisy0qny7+S5mgwkFcDslnrc3zUSv2k/v4J7U961P5TKVuZN8H5WiEiI5sfpV0MnOE6eNokqZviRkJnDw1kGalm9KfGY8aoUajaLwmPdF7WPi3xPZF7WPQNdAlry8hL41+7Lh9N1iIzi0Bi1TDkxhysEp2CnsmN1lNm/Vf8ummufHoo/x2Z7PmNVpVqFMUYB3G7xLE/8m+er5S/z3kIS9hFxJvELHSh2L3KYkadBOKidSdCkPNZaXqr3EzKMzWX95Pf1q9bN5P7VCzeo+q6k88wXuqSbirf+mUHNmWyxrQRBo4t+EJv5NmNttLjuu72DbtW3sv7WfO6a/ENX/zAREARkuKHHF3sGLTovdcv29JtFEljGLdH06Sdok4jPjSc5KznceO4UdVT2rUtOrI3V96lKvbHbYZF4rusk3u/7pOmRGQIaAGnv9SwTavYJavp9Fx4+w+/RtBDTIRAeMQgImkpDjhkL0QqWJorxLedoHtefbg98yThjH5qubCXQNzGf1Hrh1gEl7JrErchc+jj781Pkn3qz3Zu71FBXBIYoi6y+vZ/T20dxMvsmrNV9leofplHUqW+y91hq0fPjXh5y4e4KhIUOpXKZyvmidHJRypSTqEo8m7IIghAGTgOpAA1EUT5TGoJ5W9CY9d9PvEuASUOR2JVnw83H0KfFCZg7NKzSnoltFfjr2E6/WfLVEDRGC3IKoqfqW8/oxxKo/xEs3MbdRBJQ8s89eac+L1V7kxWrZ3Y7S9enM3r+bX48cIF57B7U6hUAvExo7HUlZSehNekRRRCFTYKeww83OjSC3IMpoyuDt4E0553JUcK1AkFsQ/s7+FmdIepOe6Yemcyr2FFfSvXGkc272rgw7BNGLpBQZ8Sly1l3Zi1rfFjnOKMXyGIQYsmQXcDA3w1FWHsFhCw4qB0Y3Hk2ly5UYu2ssTco1YVTDUbm1Yybvn8yem3vwcvBieofpvFX/rSLbzuXlfNx53t/2PrsidxHsGczfA/+2qTZMDoduH2Lrta1s6reJGp41gOyXokKQbDOJwjzqr+I88DIwtxTG8tQTl5Fd6TAnIsUaJUmDruhWkV2RuzCL5mKn4pZKFYxuNJp3tr7Djhs76FCxQ5H7F+Tzzt14b5VIjGISseqPcTW+hrPxJVQyxSNn9jmqHPm4bQ8+blt0nPqjsP7Seo5EH2FUg1Fsv/geaTpwMDVHhuM/cf4CMkHgUIQ3Wvlh5EIcctEZlbkSJiGRVOVKKto1o1ktOYmmULKMWdgp7AgLDiMsOAyT2cSai2v47tB3nIg5QVnHsszoMIPh9YfbLOj30u/x6d+f8mv4r7ioXZjVaRZvh75tU7TLuXvn8HTwxMfRh7ZBbWlWvhm7I3dz6u4pVl9cTYBLAJ0qdaJNYBvJly6Rj0cSdlEUL0LREQOPgydVnznHRZCTtWltHCVJg67jU4dMQyaXEy5T3dP6gqw1v/0XL3Ym0DWQ97e9T/jw8BItxGbfs+5M3ODBDdP3JCsXolMeYHyTb56JhJAFpxfwWu3XaBvUlh5Bo9l4aQta+UkcTC2B7IbYJlFELdYgQ74PkxAPYiVk2OFgaolRiMbR73t23IlnTtc52CmyG2ak6dJYcHoBM4/O5EbSDSq5V2Jut7m8Xuf13G2KI12fzvRD05l6aCo6k453Qt/hs1afWW1GncO68GgmbzvMxcxfEJU3qe4VQOugEKZ2mMroRqPpu7ov5ZzLMbHFRA7fPsyai2tIyEywqSmHxH+HZ24e9yTrM+fEbdsr7W0ahy0vn8blskv+7ovaV6SwW/Pb/7DzJrN7zabLn134ZPcnTOswrUTXlO0T7o0o9mJVxCo++OsDJh4KY3dMaz5s8iGdKnUqcSPjf+vF27x8cy7EXWBdeDTHL7ujEH3Qya7gYGqJ8E+6lIiIDAfU5mCy5OfIkp9DaQ7AydSBag6vs/aVJjipnYDs9ZPZx2az4PQC0vRpNPFvwtT2U3mx6os2ly/QGXXMPzWfr/Z9xb2Me/Sq3otv2n5jcaGzIOvCo/lozSHu8j/kohtumaNJio5nXtL/MbLBSELKhjCv2zzq+9bHQeVA43KNmbRnUq7BYcnnLvHfpFhhFwRhJ2DJ9/CJKIrrbT2RIAjDgGEA5ctb7/lYHE9LfebixmFrGnSVMlUIcA1g45WNDK8/3Op2RfntO1fuyoj6I5h+eDr1fetjZ2ieK6wuGiWCkF1rvCiRFQSBsOAwulXpxpwTc5h2aBpd/+xKoGsg/Wv1p3eN3tT2rl1IOAqKeOtqniw/dju3z2l0srbI8ElbXwLJWclkGjLzdX+qUqYK269vZ8qx0+gMKhSyshi4nduEOxsRg3CXVMUazEI6dqbaOJhboVHK+bhTTewUdqyKWMXck3PZeWMnSpmSsOAw3mv4Hg38Glj9PgpiMBn44+wffLH3C6JSomhZoSXr+q6zeSHzZvJNpm6/gc5gh4OsDXbmf/zoBk/UxlDO3jtLgGsALQNa5u6jVqi5k3aH2t61gX9/5izx9FKssIui2K40TiSK4jxgHkD9+vWLT+OzwpOsz5zj5sgyZhGTbPkhKuk4BEGgd/Xe/HD0B+Iz4q22RCvObz+j4wzOxZ1jwJrX8TFORK5/ASBfo2lbZjcapYYPGn/AOw3eYc3FNfwW/htfH/iar/Z/hb+zP22D2tK8fHMa+DXg8m0nJqy7mG/WsvjIrULHLNi82lpJ5OhkLR+vOU5U6kV8PZKIiI/gXNw5Tsee5nrSdYbUHcJvL/6We9y6PnXZcWMHkWlH0NAImWiPSUhELrphFOIQ0aEU/TGTiYsxLLeuup+rhr5NZBxKmMnw738nLiMOf2d/vmz9JUNfGFrsGkq+azMZWHJuCV/t+4rrSdep71ufud3m0qFiB5uENiYthuGbhhOTFsO19ArYC81yRR3AjI5k4xWqlsl24+VY5SsurGDuybm4qF2KbLsn8d/kmXPFPMn6zK52rgAkaZPwdXUvtXEMDhnMtMPTmH9qPuObj7e4TXF+e7VCzfq+6/Gf2oA7si/wkI/O9TXnxdbZjUquom/NvvSt2Zd76ffYeGUj265tY8PlDSw8vRAAASUKmS8KlS8K0RO56I5cdEEmOiKgQUCNIMoAgXtZZvZF2bHz0i1+OxhBlikNsyIVk5CMiSRMQjxGWRwm4T7v7+Gf4wtUcq9ESNkQhoQMKRRFEuAaQKhvKEvtZqHJbIQMR8ykI2BHpmwnavM/90ashNpUCaUyjdYh1zlzfwOj/j6GQqbgBa+2uOtaoL1Xk62HHKnpZKJnSPHfmc6oY9GZRXxz4BsikyN5oewLbOi7gW5VupXIcp53ch4VXCowqOps3rr1LQmqafjqfkFAjogJEQP2cneqemRfiyAIiKLI5qubebv+2/Su0dvicaU+of9tBFtqYFjdWRBeAn4EPIFk4LQoikUHeZNtsZ848XCRkQV925C/+cHjRGfUYTfZjkktJ1HHZWipjqPzks6ciDlB5HuRVutt2/Kwlh+7nDjVl+jkF3A29MbVOCBf9x/Iri0fOcVy44ziMItmriRe4UTMCUauWIdBdhujEJttIf/T+LokCKIGueiGQvRALnqhEL1Rir789c6rVPWoalP0SctfX+Lk7dtoheu4GvrjZOqMRimnVz0/dlyM5Eb6Hox2B0kTT2ESjdT2rs3rtV+njNCWb7fElug7TNOlMe/kPGYcmUFMWgyhvqFMbDGxxIKeY3l/s/8bohOV7DpZE63BRJzqK5Tm8rgZs0v0ypR3CAr6mx2DljJpzyS8Hb0ZETqiyGM/yWdE4vEiCMJJURTrF7fdo0bFrAXWPsoxSsqTrM+sVqjxc/LjetJ1PmtVuuOY1HISjX5rxJQDU/iqzVcWt7HFb+/v6omQ/BX3lb+QqlxFlvwMZfTvoxIfNKHwddU8tEUnE2RU86hGNY9qzNnim2/WYiYTk5CKmXREIQsRHSJmQMRJrWLegEa89ms4gqhBJjoiwwkZhaN4/Fw1hJS1wWz+h52DV/Dzgb0sPyRyN0uPh0sWDatHEp75I+HGHRhUBio4VWB4zf+jX61+uT7pplN227xeE5MWw49Hf2TOiTmk6FJoHdCahS8upF1QO5sF3Wg25oY55uyTpk9jw/lYZIbshXM3wxvcU43HydQZNV40qXWTUwnn6Li4I652rgyrN6zY8zwt61AST45nzhUDT7Y+c7BXMGfvnS31cTQs15DXar/Gdwe/o2/NvhbLwtpCjstGMLyLnbku95VzuKsehZOpGy6GPjgq3WldzbPYiB5Li6J/X4rP9yIo6B6SYY9acMAMmMwPZoJKucDUHnVoG+RHkLNgtY4MWA4LXRcezecbL5D0T7NpV40yX/0VhUxBy6oeZMi2sOnKJo7cOcKJMyKBroGMajiK3jV609CvYSEBtmW95mTMSX44+gPLzy/HJJp4ufrLjGkypkQLq1qDlnG7xiEX5IQFh+VbUB1QewDT9nXGU2iEUvRDKZZFYw4lVbGKMoa3qeJtT0SyHWObjbVY/7+48dvyd4nnj0dyxTwsj+KKedJM2D2BKQemkDw2+aFblFkjPiOe4J+D8XH04cjQIzYnwRQkryg7aDKJZQGJ4nbkgh09Kg3k1q2WJKQUHntOhyhLU/mC5EztofCsxdLf8r4wCh47b9vBgjOHdeHRjFl1Jl+hMgBkCfRomESS+SQ7b+wkNj0WgHpl69G9SnderPYidbzrFGlNN52y20pTawWjut3np+M/cej2IRxVjrwR8gbvNniXiu4VrR7PEkazkdfXvo6jypEXyr7Apiub6FalG8PrDc8dm99Xr5CiS8LV0B8FHmTI92AilepOr7BoWIUSn9PadeV8vxLPLra6YiRhLyE7ru+gw+IObOm3hc6VO5f68bdf207nJZ0JCw5jaa+lJY4ht0ZEfARf7P2ClRErMZtBY26Ao7E9GvMLuQW6cnzv1oShIA8rFCVxAzWdsps7yRkYhDvoZJfQySLQyc5jlGULuYe9B+2C2tGxYkc6VuxoU92VvOPI+5IxCLHoVDsw2u0iRZ9AJfdKjAwdyeC6g3GxcynxdUJ25mnP5T05/EZ2uedNVzax7do2Wge0zu1itfJkJG9uGIHJbEYh+pAu346nOICfX3r/oWaEko/9+eVf8bH/F2lWvhn2Sns2Xtn4WIS9Y6WOTGk3hY93foyPgw8/dPqhVOKTa3jWYFnvZXyT9A3NZo8l1rgdrfoIgmiPxhSKxlyPQMfshhC2TtkfdmpflAvLZDZx7f41ztw7w6m7pziVuQ2d3TVEIbvmu0x0Rm2ugZO+OxpzLW5/OvKhX349Q/zQm7KYuH0ht3SbyZKHI0NGt8BuvF3/bTpU7PDIL1ZvR2887D1YeHohg+oOoln5ZsSkxbA3ai8tA1riYe9BWL1AtIbv+Hb3Vm5r91BVPZavOoc9tAhLfUIlJGEvIRqlhq6Vu7IyYuVj60ozpskYYtNj+f7I95hEE7M6zyo1yz3QLZDZXWcwdk04SaYTZMgPopUfJ1Oxl0Q9lJ36EUaHSph0ASjNASjN/shxzy2ulZeHDTE1i2Zi02OJSo7iRtINrt6/ypXEK1xMuMjF+IvoTDoAlDIlKkUADobmqM1VUZuroxD9crNK/Vw1D3VfRFHkeMxxFp1ZxJ/n/iTJmER59/IMqTuJISFD8Hfxf6jrsnausBphHLh1gB5Ve+CucaeOdx0i4iNIzkrGRe3C+bjz9GtQi9cb1QI+KpXzSn1C/9tIwv4QDKwzkJURK1l/aT1hwWGlfnxBEJjeYTpyQc60w9OITotmUc9Fuanvj0rOA//5RhVJmaGIBjMGIZIs+RnS0y8hqM+Rptz1YDyi6p9QRHdkohtynJGJjrSqWJHZxy6iVqiRC3JERExmE3qTHq1RS4Y+g1RdKklZSSRkJhCXEcfd9LvEpMVgNBsfHB+BCq4VqOZRjbaBbanpVZM63nWo4VmDrecSLPrYlTKhxIXKrt2/xp/n/mTJuSVcSbyCncKOl6q9xKC6g2gb2NbmsgElQRAEWlZoyenY0yw8vZAPGn9Aw3INGbVtFG+EvMGGyxswi+aH7pgkIWEJycf+EJjMJqr8VAVPe08Ov3H4saZyzzo6i9HbR1PZvTLLei8rVQEoapFtWCsPpu7ewd2MG9lx6rJ7mEjMTigSUhGFTJvO4aB0wE3jRhlNGTwdPCnrWBZfJ1/Ku5SngksFAt0CCXILKrK4VnFRMUURmRTJyoiVrLiwgpN3TyIg0DKgJf1r9SesRthD+84tIYoi+6L2sejMIuZ1n5fvRbH35l7G7x7PmCZjqFqmKm9vfps5XecUWR9IQqIg0uLpY+aXE7/w9ua32dp/K50qdXqs59pzcw/9VvcjITOBCS0m8HHTjx+qnV5BAsduxtK3nzeBydpC3OSXgmkf7IrWqEVn1GESTQgIyGVyVHIVdgo7HJQOj8UKLgpRFDkfd551l9ax9tJawmPDAQj1DeWV4Fd4peYrD9U8vCjMopnNVzbzzYFvOHznMF4OXuwdtJdqHtXybbf+0no2XN7AoTuHGNNkDENChpTqOCSefyRhf8zoTXqqz66OvdKe8OHhD91N3lYSMxN5d+u7LD2/lMrulZnafio9qvZ4pNmCrWFxT3t6epYxi70397Ll6hY2XtlIZHIkAI3KNaJX9V70qt6LQLfAx3LeJWeXMP3wdC4mXKSCSwU+bPIhb4S8gUZpef3BYDKgkCmkgl0SD4UUFfOYUclVTGs/jZdXvMyMwzP4qGnpLHpZo4x9Gf7s9ScD6wzk/e3v03N5Txr6NWRCiwl0qdzloRYRS1I3/mlCFEUi4iPYcWMHf13/iz0396A1arFT2NEuqB1jm42le5XuxYY+PuwLKy4jjl9O/MLs47OJy4ijrk9dFr+0mD7BfYpteCE1xJD4N5As9kdAFEV6rejF5qubOfHmCWp51/pXzmswGfj9zO98ue9LbqXcomqZqowIHcGA2gNym4DYSnHiZmtMtC0i+bBCahbNXIy/yP5b+9lzcw97bu7hXsY9ACq7V6ZTpU50qtSJ1gGtrVrKlq67pLHep+6eYtbRWSw9vxS9SU+Xyl34oNEHtAlsI1ngEv8KkivmXyIuI446v9TBRe3C0aFHS3UxrjgMJgMrLqxg5tGZHI85jlqupmuVrrwS/AqdK3UulSgaW9w1tohkSYQ0SZvEiZgTHI0+yuE7hzl8+zBJWUkA+Dr50jqgNW0C29AuqB3lXR6utr+tbiidUceqiFX8fOJnDt0+hIPSgYF1BvJuw3cL+dAlJB43kivmX8LLwYvlvZfT5vc29F3dlw19N/xr022lXEn/2v3pX7s/4XfDWXh6IcsvLGfNxTWo5CpaVGhB+6D2tApoRYhPyEONy5a6I7YUnbK0TabBwJfb9qJwcOZM7JncpKTrSddzt6nuUZ2Xq79MU/+mtKjQgiC3oFKxjou7rquJV5l/aj4LTi8gITOByu6VmdFhBoNDBueWb5aQeFqRhL0UaFGhBXO6zmHYpmEM2TCEhS8u/NejQULKhhBSNoQZHWdw8PZBNl7eyJZrW/h458cA2CnsqFe2HvXK1qO2d21qeNagSpkquGvcixRKW+rfFyWSRrORu2l3uZF6AoP8HkbhLgYhBqPsDgYhmlv6LLovzd4+yC2IEJ8Q3gh5g/q+9Qn1C31sImrpuszosHM6SZvfp/P3zb+RC3K6V+3OiPojaBvUttSSxCQkHjeSK6YUmbxvMhP+nsCA2gP434v/e+yRMrYQmx7L/qj9HLp9iOMxxzkde5oMQ0bu5y5qFyq4VsDf2Z+yjmXxdPDEXeOOi9oFJ7UTZ25lsvhIDHqjgIAMETNqBQxoXI6QCg5kGjKZtOkkSdpkzKRjEtIwCymYhCSQJWESkjCJeSx1UUAuev5TybAcnnYVWTSgN7W8a+Gsdn4s98CSbx9g3JpzZBqM6IUrpCt2kinfh1nIINA1kDdC3mBwyOB8rfgkJJ40ko/9CZEj7l0rd2VZ72WlXgHyUTGLZiKTIomIj+Dq/avcSLrBrZRb3Em9w930uyRkJuTLCi0RohI5TshEF1S407BCRRoHVMbf2Z/oRAcWH8jCZPDILTr2bxSmsubbf7+jC/ui17H28lK04m1kqKjh2h4xozXpqVXwc3V46sI6JSQkYX+CzD0xl5FbRlLdszpr+qyxqUP904IoiqTp00jJSiFdn56bgGQwGzCLZmSCDLmQnYSkVqixV9rjpHJiz6U0Zu289ViiYh6FvIukJpLIkB8gU74PnfwikO1GG1B7ABpjU77aGCVVRJR4qpGE/Qmz4/oO+q7ui8Fk4OeuP9O/Vn8pJO4J4D92MZnyw2TID6CTnQfBjNJcAQdTS8I//JwA1wBAqmEu8WwgRcU8YdpXbE/48HD6r+nPgLUDWH1xNT91/gk/Z8n6e9xEJkXmlhS4ozkAiCjM5XAx9sHe1ByVWAE/V02uqIPUdUji+UIS9sdIeZfy7Bm4hxmHZ/Dpnk+pNrsaE1tMZFTDUUUWvZIoGSaziaPRR9l8ZTMbrmzgfNx5AGp51eKVKu9zLKIKJkO53HK/lrJrbYn+kZB4VpBcMf8SN5Ju8N6299h0ZRMVXCrwactPGVB7gJRi/pDEpsfy1/W/2H59O9uvbSdRm4hckNO8QnO6V+lOz2o9CXILAmzPipW6Dkk87Ug+9qeUnTd2Mm7XOE7EnKCCSwU+aPwBg+sOLrVa688rqbpU9kftZ1fkLnZF7sptKO7l4EXHih3pUrkLHSt2LHFJhbw87cXOJCQkYX+KEUWRzVc3M+XAFA7ePoiz2pnXar3GGy+8QYhPiLTISnY1y0O3D7Evah97o/Zy6u4pTKIJtVxN0/JNaR/Ung4VO1DXp26pJw7ZKvDSi0Di30YS9meEo3eOMvv4bFZcWIHOpCPYM5i+NfvSq3ovqnlU+0+IvNFs5HzceY5FH+PonaMcunOISwmXgOwqmg38GtCqQitaBbSiiX8Tmwt9PQwlKXomuW4k/m0kYX/GSNImsfzCcpacW8KBWwcAqOReiS6VutChYgeaV2j+2DIz/020Bi0X4i9wOvY04XfDCY/N/i/LmAVAGU0ZGpVrRFP/pjQt35RQ39DHKuQFsTXsUQqPlHgS/CvhjoIgTAW6A3rgOjBYFMXkRznmfxU3jRtv1X+Lt+q/RXRqNOsvr2fTlU3MOzWPWcdmIRfk1PGpQ5NyTWhYriEvlH2BKmWqPBVlCyyRpE160KQ6/iIRCRFExEdw7f41zKIZACeVE3V96vJWvbcI9QulgV8DKrpVfKKzFFvDHqXwSImnmUdVhR3AOFEUjYIgfAuMAz5+9GH9t/Fz9mNE6AhGhI4gy5jFwVsH2Ru1l/239rPg9AJ+Ov4TkF3Yq5pHNap7VKdKmSpUdKtIgGsA/i7ZdV9Ko32eJbQGLfcy7nE3LbsxdXRaNLdTbnMz5SY3k29y/f713DK7AHJBTuUylanlVYu+wX2p7V2bOj51CHILeuoKa9ka9iiFR0o8zTySsIui+Feefx4Bej/acCQKYqewo21QW9oGtQWy/dGXEi5x6u4pzt47y4X4Cxy6fYhl55chFuhg6mbnhpeDF2Xsy+Bq54qz2hlHpSP2SnvUCjVKmRK5TI5MkGEWzZjMJoxmIzqTDq1BS4Yhg3R9Oqm6VJKzkrmvvU//80tSAAAG5klEQVSiNpF0fbrFcfo7+xPoFkhozVAqulWkknul7BeOe0VUctW/cr8eFVu7Sj2r3ack/huUmo9dEISNwHJRFBdb+XwYMAygfPny9aKiokrlvBLZZBmziEqOIiolitspt4lOi+Ze+j3iM+NJ1CaSnJVMqi41u/6LQYvOpMNgMuSrvCgX5ChkCtQKNRqFJrsOjNoJZ7UzLmoX3DXueNh74GnvibejNz6OPvg6+eLn5IeHvcdzs9ArRcVIPK2U2uKpIAg7AR8LH30iiuL6f7b5BKgPvCza8KaQFk+fbiTBkpB4Oim1xVNRFNsVc6KBQDegrS2iLvF0UzCMLzpZy7g15wAkcZeQeEZ4pJUrQRA6kb1Y2kMUxczSGZLEk6SoNncSEhLPBo8akvAT4ATsEAThtCAIv5TCmCSeIFIYn4TEs8+jRsVUKq2BSDwdSGF8EhLPPk9XELHEE2dMx6polPkbcUthfBISzxZPZ9qixBMjZ4FUioqRkHh2kYRdohA9Q/wkIZeQeIaRXDESEhISzxmSsEtISEg8Z0jCLiEhIfGcIQm7hISExHOGJOwSEhISzxmSsEtISEg8Z0jCLiEhIfGcIQm7hISExHOGJOwSEhISzxmSsEtISEg8Z0jCLiEhIfGcIQm7hISExHOGJOwSEhISzxmSsEtISEg8Z0jCLiEhIfGcIQm7hISExHOGJOwSEhISzxmSsEtISEg8Z0jCLiEhIfGcIQm7hISExHOGJOwSEhISzxmPJOyCIHwpCMJZQRBOC4LwlyAIvqU1MAkJCQmJh+NRLfapoijWFkWxLrAJ+LQUxiQhISEh8Qg8krCLopia558OgPhow5GQkJCQeFQUj3oAQRAmA68DKUDrRx6RhISEhMQjIYhi0Ua2IAg7AR8LH30iiuL6PNuNA+xEUfzMynGGAcMAypcvXy8qKuqhB/1fZl14NFO3XyYmWYuvq4YxHavSM8TvSQ9LQkLiX0AQhP9v735C4yjjMI5/H5aICwo5WND+oXoowRK1hSAVb7XQKFK1IuhBBL0ICgpStPTkSSHgSUEExUtRBFsVi8QIlV78FzXWliRSBDGtUEWKLQZt05+HnZZEkt1kZ5o38+b5QCAzO2SelyQPs/O+u/ttRAx0PK5TsS/hhBuBQxHR3+nYgYGBGB0dreS8q8kH359k74EfmT4/c3lfs6fBS7tvcbmbrQKLLfayq2I2zdrcBUyU+XnW3tDw5JxSB5g+P8PQ8GSiRGa2EpW9x/6ypD7gIvAL8GT5SLaQU2eml7TfzFanUsUeEQ9WFcQ6W9vb5OQ8Jb62t5kgjZmtVH7laY3s2dlHs6cxZ1+zp8GenX2JEpnZSlR6uaMtn0sTpF4VY2btuNhr5v6t61zkZtaWb8WYmWXGxW5mlhkXu5lZZlzsZmaZcbGbmWXGxW5mlhkXu5lZZlzsZmaZqexte5d0Uul3Wm8aVkfXAX+kDlExj6kePKb6uFLj2hgRazodlKTY60zS6GLeD7lOPKZ68JjqI/W4fCvGzCwzLnYzs8y42JfujdQBrgCPqR48pvpIOi7fYzczy4yv2M3MMuNi74KkIUkTko5KOiipN3WmsiQ9JOm4pIuSar1KQdKgpElJJyS9kDpPWZLeknRa0rHUWaoiaYOkw5LGi7+7Z1JnKkvS1ZK+lvRDMaYXU2VxsXdnBOiPiFuBn4C9ifNU4RiwGziSOkgZkhrAa8DdwGbgEUmb06Yq7W1gMHWIil0AnouIm4FtwFMZ/J7+AbZHxG3AFmBQ0rYUQVzsXYiITyPiQrH5JbA+ZZ4qRMR4REymzlGB24ETEfFzRPwLvAvclzhTKRFxBPgzdY4qRcRvEfFd8f1ZYByo9UeDRcu5YrOn+EoyieliL+9x4JPUIeyydcCvs7anqHlh5E7SjcBW4Ku0ScqT1JA0BpwGRiIiyZj8macLkPQZcP08D+2LiA+LY/bRekq5fzmzdWsxY8qA5tnnpV8rlKRrgPeBZyPir9R5yoqIGWBLMe92UFJ/RCz73IiLfQERsaPd45IeA+4F7oqarBntNKZMTAEbZm2vB04lymJtSOqhVer7I+JA6jxViogzkj6nNTey7MXuWzFdkDQIPA/sioi/U+exOb4BNkm6SdJVwMPAR4kz2f9IEvAmMB4Rr6TOUwVJay6tkJPUBHYAEymyuNi78ypwLTAiaUzS66kDlSXpAUlTwB3AIUnDqTN1o5jUfhoYpjUh915EHE+bqhxJ7wBfAH2SpiQ9kTpTBe4EHgW2F/9DY5LuSR2qpBuAw5KO0rrAGImIj1ME8StPzcwy4yt2M7PMuNjNzDLjYjczy4yL3cwsMy52M7PMuNjNzDLjYjczy4yL3cwsM/8BFevbT33ObgkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#看看目标分布的效果\n",
    "X=np.random.multivariate_normal(mean=u, cov=sigma, size=200)\n",
    "utils.plot_contourf(X,lambda x:utils.gaussian_nd(x,u,sigma),8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "建议分布使用以当前维度的取值为均值，方差1为一元高斯分布，这样它们在该维的建议分布取值对称：   \n",
    "\n",
    "$$\n",
    "q(x_j^{'(i)}\\rightarrow x_j^{(i-1)}\\mid x_{-j}^{(i)})=q(x_j^{(i-1)}\\rightarrow x_j^{'(i)} \\mid x_{-j}^{(i)})\n",
    "$$  \n",
    "\n",
    "对于计算接受概率就更方便了：   \n",
    "\n",
    "$$\n",
    "\\alpha(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})=min\\{1,\\frac{p(x_j^{'(i)}\\mid x_{-j}^{(i)})}{p(x_j^{(i-1)}\\mid x_{-j}^{(i)})}\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "#采样的样本量\n",
    "nums=1000\n",
    "count=0\n",
    "points=[]\n",
    "#采样x0\n",
    "point=[np.random.randn(),np.random.randn()]\n",
    "points.append(point)\n",
    "while count<nums:\n",
    "    for k in (0,1):\n",
    "        new_point=copy.deepcopy(point)\n",
    "        #按照q(x,x')\n",
    "        new_point[k]=np.random.randn()+point[k]\n",
    "        #alpha(x,x')\n",
    "        alpha=min(1.,utils.gaussian_1d(new_point[k],0.5*new_point[(k+1)%2],0.75)/utils.gaussian_1d(point[k],0.5*point[(k+1)%2],0.75))\n",
    "        #从(0,1)均匀采样一个u\n",
    "        u=np.random.random()\n",
    "        #判断是否接收新点还是旧点\n",
    "        if u<alpha:\n",
    "            point=new_point\n",
    "    points.append(point)\n",
    "    count+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.plot_contourf(np.asarray(points[-400:]),lambda x:utils.gaussian_nd(x,u,sigma),8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 四.小结\n",
    "\n",
    "效果看起来还不错，然后我们继续想一种情况，如果目标分布$p(x)$的采样困难是由于随机变量维度太高造成的，而它在单个维度（满条件概率分布）上采样是相对比较容易的，那么我们可以用单维度上的满条件概率分布替换建议分布来采样，即：   \n",
    "\n",
    "$$\n",
    "q(x_j^{(i-1)}\\rightarrow x_j^{'(i)} \\mid x_{-j}^{(i)})=p(x_j^{'(i)} \\mid x_{-j}^{(i)})\n",
    "$$   \n",
    "\n",
    "这种情况下又会发生什么神奇的事情呢？请看下一节Gibbs采样"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
